Suppose I have two simple, integrateable functions of variable t such that

$\displaystyle \int_{0}^{t_1}f(t)dt = \int_{0}^{t_2}g(t)dt$

I believe that if $\displaystyle f(t) \leq g(t)$ for all t then $\displaystyle t_2 \leq t_1$

Any tips on how to prove this? Thanks