If is an eigenvalue then , so . But as far as the integral is concerned, x is a constant, so we can take out the factor and get . But then the integral is a constant, and we are left with two possibilities. The first is that and the integral are both 0. The second is that f(x) is a nonzero constant times , in which case you can plug that formula for f into the integral, and you should then find that (if I've done the integration correctly).