Chapter 5.10, Problem 43ES

Let $F\left(x\right)={\displaystyle {\int }_0^{x}f\left(t\right)dt}$ , where $f$ is the function graphed in the accompanying figure.

(a) Where do the relative minima of $F$ occur?

(b) Where do the relative maxima of $F$ occur?

(c) Where does the absolute maximum of $F$ on the interval $\left[0,5\right]$ occur?

(d) Where does the absolute minimum of $F$ on the interval $\left[0,5\right]$ occur?

(e) Where is $F$ concave up? Concave down?

(f) Sketch the graph of $F$ .