If a bounded operator $\displaystyle T:L^2([0,1],\mathbb{C})\rightarrow L^2([0,1],\mathbb{C})$ is defined by

$\displaystyle Tf(x)=\int^{1}_{0}(x-y)f(y)dy$

What is its adjoint?

I'm assuming the usual inner product on $\displaystyle L^2$

$\displaystyle \langle f,g\rangle=\int^{1}_{0}f(x)\overline{g(x)}dx$

Can anyone give me some help finding this? I'm not too good at manipulating integrals. (Not asking for the definition of adjoint)