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[tex]\displaystyle \frac{dF(x)}{dx}=f(x)\\dF(x)=f(x)\,dx\\\\\int\limit^b_aF(x)f(x)\,dx=\int\limit^b_aF(x)\,dF(x)\\\int\limit^b_aF(x)f(x)\,dx=\left\frac12F^2(x)\right|^b_a\\\boxed{\boxed{\int\limit^b_aF(x)f(x)\,dx=\frac12\left(F^2(b)-F^2(a)\right)}}[/tex]