Chapter 8.1, Problem 60E

To determine

To show: The function $h\left(t\right)={\displaystyle \underset{0}{\overset{t}{\int }}f\left(u\right)du}$ is of exponential order if $f\left(t\right)$ is a piecewise continuous function on the interval $\left[0,\infty \right)$ and of exponential order $b$ for $t>T$.