Let [tex]$f : [0,1] \rightarrow [0,1]$[/tex] be a continuous function (not necessarily differentiable) such that [tex]$f(f(x)) = 1$ for all $x \in [0,1].$[/tex] Prove that
[tex]\[\int_0^1 f(x)\,dx \ \textgreater \ \frac34.\][/tex]