(b) Restricted Function: Let g be a bounded function on [0, 1] and assume that its restriction to the interval [1/n, 1] is Riemann integrable for every n > 2. You are to show that g is Riemann integrable on the entire interval [0, 1]. Hint: You're given to let € > 0 and M > 0 be constants such that g(x)| ≤ M for all z in [0, 1]. Choose n > 2 such that <3 and note that the supremum and infimum of g on [0,1/n] differ by less than ². 3M You are to show that g is Riemann integrable on [1/n, 1] and find an appropriate partition of [0, 1].

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