设函数 $f(x, y)$ 连续，则 $\int_1^2 \mathrm{~d} x \int_x^2 f(x, y) \mathrm{d} y+\int_1^2 \mathrm{~d} y \int_y^{4-y} f(x, y) \mathrm{d} x=$
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. $\int_1^2 \mathrm{~d} y \int_y^2 f(x, y) \mathrm{d} x$