Answer
$f(x)=\tan x+1.
$
Work Step by Step
We have
$$
f(x)=\int_{-\pi/4}^x\sec^2\theta d\theta =\tan \theta |_{-\pi/4}^x=\tan x+1.
$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 5 - The Integral - 5.5 The Fundamental Theorem of Calculus, Part II - Exercises - Page 262: 10
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