设∫f(x)dx=F(x),则F(0)=0,F(1)=A,
∫[∫f(x)f(y)dy]dx
=∫f(x)[∫dF(y)] dx
=∫[A-F(x)]dF(x )
=A∫f(x)dx -(A^2)/2
=(A^2)/2