Let $f$ be a differentiable function such that $f(f(x)) = x \forall x \in [0,1]$. Suppose $f(0) = 1$. Determine the value of $\int_0^1 (x - f(x))^{2016} dx$.
I noticed that $f(x) = 1-x$ satisfies the properties, and putting $f(x) = 1-x$ and substituting $x - f(x) = z$ , I can calculate the integral. But is there any other way which does not require the assumption that $f(x)=1-x$?
