A bounded function defined on a closed bounded interval

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If f is a bounded function defined on a closed bounded interval [a, b] and if f is integrable on each interval [a, r] with a < r < b, then prove that f is integrable on [a, b] and  ( integral from a to b ) f(x) dx = lim r →b ( integral from a to r ) f (x) dx .

Reference no: EM13535320

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