Question: Let f(x) = x2 for 0 < x < 1. For the partition Pn := (0, 1/n, 2/n, . . . , (n - 1)/n,

Let f(x) = x2 for 0 < x < 1. For the partition Pn := (0, 1/n, 2/n, . . . , (n - 1)/n, 1), calculate L(f, Pn) and U(f, Pn), and show that L(f) = U(f) = 1/3. (Use the formula 12 + 22 + ∙ ∙ ∙+m2 = 1/6m(m + 1)(2m + 1).)

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