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suppose f is a continuous non negative function if int(f(x),x=a..b)=0 show that f(x)=0

what i have done is used mean value theorem to show some point c is such that f(c)=0. from here though i can only think of a verbal argument (since f is non negative) to explain why f(x)=0.

i am wondering if there us an obvious use of the fundamental theorems here that im not seeing, or just some simple method.

thank you for any help