Two wrongs don't make a right... or do they?

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Given that F(x)=f(x)dxF(x) = \int f(x) dx and C=0C = 0, can we say that F(a)>0F(a) > 0 if f(x)=1xf(x)=-\frac{1}{x} and a<0a < 0 ?

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