: Let f [a, b] → R be a bounded function. Suppose there exists a partition Pn of [a, b] such that lim [U (f; Pn) — L (ƒ; Pn)] = 0. nx (a) Show that f is integrable on [a, b]. (b) Conclude that the value of the integral of ƒ on [a, b] is [s = lim U (f; Pn) : = lim L (f; Pn). n→∞ n4x

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