(4) Suppose f(x) is increasing on [a, b]. Let Pn = {0, 1,...,n}, where xk = a + k (b − a), k = 0, 1,..., n. Prove that and Lºra a 0 ≤ U(Pn, f) - ["F(x) dx ≤ b = ª (f(b)-f(a)) n f(x) dx = lim U(Pn, f). N→∞

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