Recall that if P = {xo,...,n} is a partition of [a, b], M₁(f) = sup{ƒ(x),xj–1 ≤ x ≤ xj}, m;(ƒ) = inf{ƒ(x), X;−1 ≤ x ≤ x; }, n n U(ƒ, P) = ΣM;(ƒ)(x; — xj−1), L(ƒ,P) = Σm;(f)(x¡ — xj-1). j=1 j=1 Suppose f is a function that is increasing and bounded on [a, b]. a) Let P = {xo,...,n} be a partition of [a, b]. For j = 1,..., n, find m, (f) and M; (f). b) Use the information from a) to find U(f, P) - L(f, P). c) Show that f is integrable on [a, b].
