Answer
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Work Step by Step
Letting $u=x-c$, we have $du=dx$ and $x=a\to u=a-c, x=b\to u=b-c$.
Start from the left-hand side
$LHS=\int_a^b f(x)dx=\int_{a-c}^{b-c}f(u+c) du=RHS$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 5: Integrals - Section 5.6 - Definite Integral Substitutions and the Area Between Curves - Exercises 5.6 - Page 306: 89
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