Answer
$$\iint_{D} f(x,y) dA=\int_{0}^{1} \int_{x}^{1} f(x,y) \ dy \ dx$$
Work Step by Step
We can define the domain $D$ in the Type-1 using the vertical cross-sections as follows: $
D=\left\{ (x, y) | x \leq y \leq 1, \ 0 \leq x \leq 1 \right\}
$
and we can define the domain $D$ in the Type-II using the horizontal cross-sections as follows: $
D=\left\{ (x, y) | 0 \leq x \leq y, \ 0 \leq y \leq 1 \right\}
$
Therefore, $$\iint_{D} f(x,y) dA=\int_{0}^{1} \int_{x}^{1} f(x,y) \ dy \ dx$$
