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