Chapter 4.3, Problem 3E

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 $g\left(0\right),g\left(1\right),g\left(2\right),g\left(3\right),$ and $g\left(6\right)$.

(b) On what interval is g increasing?

(c) Where does g have a maximum value?

(d) Sketch a rough graph of g.