Supposeg 2 [R > IR is defined by: arctan(tan( % ) ) , x is not an odd integer g(x) = . . 0, 2: IS an odd Integer a) Prove that g(x) is integrable on [0, a] for any a E R. You may use the previous question, as well as the analagous result for right endpoints, without proof. b) Prove that there exists a function f (x) with f ' (x) = g(x), except at odd integers x. Write your function as an integral. Prove that your function f satisfies that f ' (x) = g(x) if x is not an odd integer. C) Is it possible for any function f with f ' (x) = g(x) (except possibly for odd integer x) to be differentiable at odd integers x