Let A = : ne Zandn21 = 1737. Let f (z) = 0 if I E A 1 if re A In this question we will prove that f is integrable on [0, 1]. (a) Prove that 18 (f) = 1. (b) Prove that for every positive integer n, and for every e > 0, there exists a partition P of [0, 1] such that Up(f) > 1 - - -E. Note: this question involves two arbitrary values, namely, n and e. So you might want to first pick a value for n, say n = 2, and show that for any e > 0, there exists a partition P of [0, 1] such that Lp(9) > 1 -- 7-6= 7 - E. Do a similar proof for n = 3 and n = 4. Doing this might make answering this part easier. (c) Prove that for every e > 0, there exists a partition P of [0, 1] such that Lp(f) > 1 - E. Hint. Use part (b). (d) Show that Io (f) = 1, and conclude that f is integrable on [0, 1]