I need help with part (b.)

8. [5 marks] Suppose that f : [a, b] - R is a bounded Riemann integrable function. Define the area function for f by Af (x) : f(t) dt. a a Prove that for any x0 E [a, b), Af is right continuous at X0. b Give an example of a bounded Riemann integrable function f and a point to such that Af is not differentiable at co. (You should explicitly calculate Af so that it is clear that it is not differentiable.)