Chapter 4.1, Problem 10E

For each $f\in C[0,1]$ , define $L(f)=F$ , where
$\begin{array}{cc}F(x)={\displaystyle {\int }_0^{x}f(t)dt}& 0\le x\le 1\end{array}$
Show that L is a linear operator on $C[0,1]$ and then find $L(e^x)$ and $L(x^e)$ .