Answer
See explanation.
Work Step by Step
For every chosen partition:
(b) $\sum_{k=1}^{n} \Delta x_{k} f\left(x_{k}^{*}\right)=1$
Take the limit:
$\lim _{\max \Delta x_{k} \rightarrow 0} \sum_{k=1}^{n} \Delta x_{k} f\left(x_{k}^{*}\right)=1$
Using definition 5.5.1:
\[
\int_{0}^{1} f(x) d x=1
\]
