[math-fun] Amusing math problem

I recently found this problem online somewhere and with a little thought and a little luck managed to solve it. I think. ----- Let f : R —> R be a continuous function that is positive and periodic of period 1. That is, f(x+1 ) = f(x) for all x. Prove that for any real number c Integral_{0 ≤ x ≤ 1} f(x+c)/f(x) dx ≥ 1 ----- —Dan