Chapter 5.10, Problem 31ES

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

(a) Find $F\left(0\right),F\left(3\right),F\left(5\right),F\left(7\right),$ and $F\left(10\right)$ .

(b) On what subintervals of the interval $\left[0,10\right]$ is $F$ increasing? Decreasing?

(c) Whose dose $F$ have its maximum value? Its minimum value?

(d) Sketch the graph of $F$ .