Suppose that a < b < c. Let f: [a, c] → R. Decide which of the following statements is true and which is false. Prove the true ones and give counterexamples for the false ones. (a) (3 pts) If f is Riemann integrable on [a, b], then f is continuous on (a,b]. (b) (3 pts) If |f| is Riemann integrable on [a, b], then f is Riemann integrable on [a, b]. (c) (4 pts) If f is continuous on (a,b) and on [b,c), then f is Riemann integrable on [a, c). (d) (9 pts) If f is continuous on (a,b) and on [b, c) and is bounded on ſa, c], then f is Riemann integrable on ſa, c]. .. #2. Let a < b and f: [a, b] → R be an increasing function. (a) (4 pts) If P = {xo, Xn} is any partition of [a,b], prove that ...) n (M;(f) – mj(f))Ax; < (f(b) – f(a))||P||. j=1 (b) (4 pts) Prove that f is integrable on [a, b].