Let f : R to R be a continuous function, and suppose that definite integral from m to n |∫(m to n)f(x)dx|≤(n-m)^2 for every closed bounded interval [m, n] in R. Then is it the case that f(x) = 0 for all x in R?(adsbygoogle = window.adsbygoogle || []).push({});

I tried using fundamental theorem of calculus but got stuck, since I only got that F'(x)=f(x)≤ 0.

Any help/suggestion would be appreciated.

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# Integrals and continuity

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