a) If f is increasing on [a, b] and P = {x0, ..., xn] is any partition

Question:

a) If f is increasing on [a, b] and P = {x0, ..., xn] is any partition of [a, b], prove that

b) Prove that if f is monotone on [a, b], then f is integrable on [a, b].
[By Theorem 4.19, f has at most countably many (i.e., relatively few) discontinuities on [a, b]. This has nothing to do with the proof of part b), but points out a general principle which will be discussed in Section 9.6.]