Suppose that is integrable on [a, b] and 0 < m (x) M for

Suppose that ƒ is integrable on [a, b] and 0 < m ≤ ƒ(x) ≤ M for all x in the interval [a, b]. Prove that

Use this result to estimate

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m(a - b) ≤ b [ f(x) dx ≤ M(b − a).