T is a bounded linear operator mapping from C[0,1] to C[0,1] with the two norm.

Find the non-zero eigenvalues of T, where

$\displaystyle (Tf)(x)=\int_{a}^{b} f(t)(x+t)dt$

You may assume all eigenvectors for non-zero eigenvalues are of the form $\displaystyle f(x)=Ax+B$