Chapter 5.3, Problem 92E

Let

$f(x)=\{\begin{array}{ll}0\hfill & \text{if}x<0\hfill \\ x\hfill & \text{if}\text{0}\le x\le 1\hfill \\ 2-x\hfill & \text{if}\text{1< }x\le 2\hfill \\ 0\hfill & \text{if}x>2\hfill \end{array}$

and

$g(x)={\displaystyle {\int }_0^{x}f(t)dt}$

(a) Find an expression for g(x) similar to the one for f(x).

(b) Sketch the graphs of f and g.

(c) Where is f differentiable? Where is g differentiable?