Let f(x) =

(0) if x< 0

(x) if 0 <= x <= 1

(2 - x) if 1 < x <= 2

(0) if x > 2

and g(x) = [integrate] f(t)dt on [0, x]

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

ii) Where is f differentiable? Where is g differentiable?

I'm pretty much stuck, and don't know how to start this question.

I know first of all that by the fundamental theorem of Calculus, g'(x) = f(x).

But from that, how do I figure out an expression for g(x) from the piecewise function?

Any and all help is appreciated here.