(a) Let be a fixed enumeration of the rationals in . For positive reals , define a function from to by setting for each and for irrational. Prove that if then is Riemann integrable. If , can be Riemann integrable? Justify your answer.
(b) State and prove the Fundamental Theorem of Calculus.
Let be a differentiable function from to , and set for . Must be Riemann integrable on ?