设函数 $f(x, y)$ 连续, 则 $\int_1^2 d x \int_x^2 f(x, y) d y+\int_1^2 d y \int_y^{4-y} f(x, y) d x=$
$\text{A.}$ $\int_1^2 d x \int_1^{4-x} f(x, y) d y$.
$\text{B.}$ $\int_1^2 d x \int_x^{4-x} f(x, y) d y$.
$\text{C.}$ $\int_1^2 d y \int_1^{4-y} f(x, y) d x$.
$\text{D.}$ $\int_1^2 d y \int_y^2 f(x, y) d x$.