Solve an integral equation

Question

How can I solve the following problem for $s(x,T)$, $s(\cdot)$ is continuous and strictly increasing in $x$.

$\int_0^T\frac{-x^3+x^2-T(1-T)x}{(s(x,T)-x)^2}dx=0$

s.t. $s(T,T)=T$