proof of existence While I was studying for my finals i found the following problem:
Let $f:[a,b]\rightarrow \mathbb{R}$ be a Riemann integrable real function, also let $\displaystyle \int\limits_a^bf(t)\,\mathrm{d}t=3$
Prove that there exist $\displaystyle t_1,t_2 \!\in \! (a,b):\int\limits_{t_1}^{t_2}f(t)\,\mathrm{d}t=1$
Could you give me any hint or a way to start the solution?

HINT: The function
$$
F(x)=\int_a^x f(t)\,dt 
$$
is continuous and $\int_a^a f(t)\,dt=0$.
