First Trust Energy Infrastructure Fund Issues Notice Regarding June 2019 Distribution

WHEATON, Ill.–(BUSINESS WIRE)–The Board of Trustees of First Trust Energy Infrastructure Fund (the
“Fund”) (NYSE: FIF), CUSIP 33738C103, previously approved a managed
distribution policy for the Fund (the “Managed Distribution Plan”) in
reliance on exemptive relief received from the Securities and Exchange
Commission which permits the Fund to make periodic distributions of
long-term capital gains as frequently as monthly each tax year.

The Fund has declared a distribution payable on June 17, 2019, to
shareholders of record as of June 4, 2019, with an ex-dividend date of
June 3, 2019. This Notice is meant to provide you information about the
sources of your Fund’s distributions. You should not draw any
conclusions about the Fund’s investment performance from the amount of
its distribution or from the terms of its Managed Distribution Plan.

The following tables set forth the estimated amounts of the current
distribution and the cumulative distributions paid this fiscal year to
date for the Fund from the following sources: net investment income
(“NII”); net realized short-term capital gains (“STCG”); net realized
long-term capital gains (“LTCG”); and return of capital (“ROC”). These
estimates are based upon information as of May 31, 2019, are calculated
based on a generally accepted accounting principles (“GAAP”) basis and
include the prior fiscal year-end undistributed net investment income.
The amounts and sources of distributions are expressed per common share.

                          5 Yr. Avg.
Annualized Current Annual Total
Fund Fund Fiscal Total Current Current Distribution ($) Current Distribution (%) Dist. Rate as a Return
Ticker Cusip Year End Distribution NII STCG LTCG ROC (2) NII STCG LTCG ROC(2) % of NAV(3) on NAV(4)
FIF (5) 33738C103 11/30/2019 $0.11000 $0.02193 $0.08807 19.94% 80.06% 7.60% 1.78%
Total Cumulative Cumulative Fiscal
Fund Fund Fiscal Cumulative Fiscal YTD Cumulative Distributions Fiscal YTD ($) Cumulative Distributions Fiscal YTD (%) Fiscal YTD Distributions as YTD Total Return
Ticker Cusip Year End Distributions(1) NII STCG LTCG ROC (2) NII STCG LTCG ROC(2) a % of NAV(3) on NAV(4)
FIF (5) 33738C103 11/30/2019 $0.77000 $0.15354 $0.61646 19.94% 80.06% 4.43% 8.02%
(1) Includes the most recent monthly distribution paid on June 17,
(2) The Fund estimates that it has distributed more than its income
and net realized capital gains; therefore, a portion of your
distribution may be a return of capital. A return of capital may
occur, for example, when some or all of the money that you invested
in the Fund is paid back to you. A return of capital distribution
does not necessarily reflect the Fund’s investment performance and
should not be confused with “yield” or “income.”
(3) Based on Net Asset Value (“NAV”) as of May 31, 2019.
(4) Total Returns are through May 31, 2019.
(5) The Fund anticipates that, due to the tax treatment of cash
distributions made by Master Limited Partnerships in which the Fund
invests, a portion of distributions the Fund makes to Common
Shareholders may consist of a tax-deferred return of capital.

The amounts and sources of distributions reported in this Notice are
only estimates and are not being provided for tax reporting purposes.
The actual amounts and sources of the amounts for tax reporting purposes
will depend upon the Fund’s investment experience during the remainder
of its fiscal year and may be subject to changes based on tax
regulations. The Fund will send you a Form 1099-DIV for the calendar
year that will tell you how to report these distributions for federal
income tax purposes. You should not use this Notice as a substitute for
your Form 1099-DIV.

First Trust Advisors L.P. (“FTA”) is a federally registered investment
advisor and serves as the Fund’s investment advisor. FTA and its
affiliate First Trust Portfolios L.P. (“FTP”), a FINRA registered
broker-dealer, are privately-held companies that provide a variety of
investment services. FTA has collective assets under management or
supervision of approximately $126 billion as of May 31, 2019 through
unit investment trusts, exchange-traded funds, closed-end funds, mutual
funds and separate managed accounts. FTA is the supervisor of the First
Trust unit investment trusts, while FTP is the sponsor. FTP is also a
distributor of mutual fund shares and exchange-traded fund creation
units. FTA and FTP are based in Wheaton, Illinois.

Energy Income Partners, LLC (“EIP”) serves as the Fund’s investment
sub-advisor and provides advisory services to a number of investment
companies and partnerships for the purpose of investing in MLPs and
other energy infrastructure securities. EIP is one of the early
investment advisors specializing in this area. As of May 31, 2019, EIP
managed or supervised approximately $6.1 billion in client assets.

Past performance is no assurance of future results. Investment return
and market value of an investment in the Fund will fluctuate. Shares,
when sold, may be worth more or less than their original cost. There can
be no assurance that the Fund’s investment objectives will be achieved.
The Fund may not be appropriate for all investors.

Principal Risk Factors: The Fund is subject to risks, including the fact
that it is a non-diversified closed-end management investment company.

Because the Fund is concentrated in securities issued by energy
infrastructure companies, it will be more susceptible to adverse
economic or regulatory occurrences affecting that industry, including
high interest costs, high leverage costs, the effects of economic
slowdown, surplus capacity, increased competition, uncertainties
concerning the availability of fuel at reasonable prices, the effects of
energy conservation policies and other factors.

The Fund invests in securities of non-U.S. issuers which are subject to
higher volatility than securities of U.S. issuers. Because the Fund
invests in non-U.S. securities, you may lose money if the local currency
of a non-U.S. market depreciates against the U.S. dollar.

There can be no assurance as to what portion of the distributions paid
to the Fund’s Common Shareholders will consist of tax-advantaged
qualified dividend income.

Use of leverage can result in additional risk and cost, and can magnify
the effect of any losses.

The risks of investing in the Fund are spelled out in the shareholder
reports and other regulatory filings.

The information presented is not intended to constitute an investment
recommendation for, or advice to, any specific person. By providing this
information, First Trust is not undertaking to give advice in any
fiduciary capacity within the meaning of ERISA, the Internal Revenue
Code or any other regulatory framework. Financial advisors are
responsible for evaluating investment risks independently and for
exercising independent judgment in determining whether investments are
appropriate for their clients.

Forward-Looking Statements

Certain statements made in this press release that are not historical
facts are referred to as “forward-looking statements” under the U.S.
federal securities laws. Actual future results or occurrences may differ
significantly from those anticipated in any forward-looking statements
due to numerous factors. Generally, the words “believe,” “expect,”
“intend,” “estimate,” “anticipate,” “project,” “will” and similar
expressions identify forward-looking statements, which generally are not
historical in nature. Forward-looking statements are subject to certain
risks and uncertainties that could cause actual results to differ from
those anticipated in any forward-looking statements. You should not
place undue reliance on forward-looking statements, which speak only as
of the date they are made. The Fund undertakes no responsibility to
update publicly or revise any forward-looking statements.


Inquiries: Don Swade (630) 765-8661