Let $f:[0,a]\times[0,b]\rightarrow\mathbb{R}$ be a continuous function. Prove a version of Fubini's Theorem:
Prove that $\int_a^b \left( \int_c^d f(x,y)dy\right) dx=\int_c^d \left( \int_a^b f(x,y)dx\right) dy$