This exercise is used in Sections *5.5, 6.2, and *7.5.a) If f is increasing on [a, b] and...

This exercise is used in Sections *5.5, 6.2, and *7.5.

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

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b) Prove that if f is monotone on [a, b], then f is integrable on [a, b]. [Note: By Theorem, 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]