设函数 $f(x, y)$ 连续，则二次积分 $\int_{\frac{\pi}{2}}^\pi \mathrm{d} x \int_{\sin x}^1 f(x, y) \mathrm{d} y$等于
$\text{A.}$ $\int_0^1 \mathrm{~d} y \int_{\pi+\arcsin y}^\pi f(x, y) \mathrm{d} x$
$\text{B.}$ $\int_0^1 \mathrm{~d} y \int_{\pi-\arcsin y}^\pi f(x, y) \mathrm{d} x$
$\text{C.}$ $\int_0^1 \mathrm{~d} y \int_{\frac{\pi}{2}}^{\pi+\arcsin y} f(x, y) \mathrm{d} x$
$\text{D.}$ $\int_0^1 \mathrm{~d} y \int_{\frac{\pi}{2}}^{\pi-\arcsin y} f(x, y) \mathrm{d} x$