Answer
$$
\frac{1}{6} (b^6-1).
$$
Work Step by Step
We have
$$
\int_1^bx^5dx=\frac{1}{6}x^6|_1^b=\frac{1}{6} (b^6-1).
$$
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 - 5.4 The Fundamental Theorem of Calculus, Part I - Exercises - Page 258: 41
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