数学已知f(x)=x-∫f(x)dt,上极限为1,下极限为0,求f(x)?

设A = ∫(0~1) f(x) dx
f(x) = x - A
∫(0~1) f(x) dx = ∫(0~1) x dx - A • ∫(0~1) dx
A = [x²/2] |(0~1) - A
2A = 1/2
A = 1/4
∴f(x) = x - 1/4