Chapter 13.2, Problem 14E

To determine

If the given assertion is true when uniform convergence is replaced by pointwise convergence.

“Let $\left\{y_n\right\}$ be a sequence of functions in $C\left[a,b\right]$ that converge uniformly to a function $y$ in

$C\left[a,b\right]$. Then, $\underset{n\to \infty }{\lim }{\displaystyle \underset{a}{\overset{b}{\int }}{y}_n\left(x\right)dx}={\displaystyle \underset{a}{\overset{b}{\int }}y\left(x\right)dx}$.”