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f is continuous if F has a finite derivative

Source: Romanian MO 2010 Grade 12

August 6, 2012
calculusderivativefunctionintegrationlimitreal analysisreal analysis unsolved

Problem Statement

Let f:R→Rf:\mathbb{R}\to\mathbb{R} be a monotonic function and F:R→RF:\mathbb{R}\to\mathbb{R} given by F(x)=∫0xf(t) dt.F(x)=\int_0^xf(t)\ \text{d}t. Prove that if FF has a finite derivative, then ff is continuous.
Dorin Andrica & Mihai Piticari
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