(a) What does it mean for a function to be Riemann integrable?
(b) Let be a bounded function. Suppose that for every there is a sequence
such that for each the function is Riemann integrable on the closed interval , and such that . Prove that is Riemann integrable on .
(c) Let be defined as follows. We set if has an infinite decimal expansion that consists of 2 s and only, and otherwise we set . Prove that is Riemann integrable and determine .