Chapter 4.3, Problem 2E

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

(a) Evaluate g(x) for $x=0,1,2,3,4,5,\text{ and }6$

(b) Estimate $g\left(7\right)$.

(c) Where does g have a maximum value? Where does it have a minimum value?

(d) Sketch a rough graph of g.