A friend of mine gave this question to me :
Find the value of $\int_0^1f(x)dx$ if $f$ is a real, non-constant, differentiable function satisfying $$f(f(x))=1-x \space\space\space\space\space\space\forall x\in(0,1)$$
The only thing that came to my mind was to form a differential equation with the given equation and find a solution but that was a dead end. If someone could give me a hint on how to tackle this problem it would be great.
EDIT: All this time wonghang and John Ma's answers had me convinced that this problem was not well thought-out. But like Sanket has pointed out, if we disregard the differentiable assumption for a while, does there now exist an $f$ satisfying the given conditions? Can someone find an example? I tried to produce one using some variants of the absolute value function but to no avail.