Iterated Integrals

Suppose $f$ is defined on $R = [a,b] \times [c,d]$ such that $\forall x \in [a,b]$, $\int_c^d f(x,y)\,\text{d}y$ exists.

$$\int_a^b \int_c^d f(x,y)\;\text{d}y\,\text{d}x$$

The inner integral is first solved, assuming $x$ as a constant, which results in a function of $x$.