设 $f(x, y)$ 是连续函数, 则 $\int_{\frac{\pi}{6}}^{\frac{\pi}{2}} d x \int_{\sin x}^1 f(x, y) d y=$
A. $\int_{\frac{1}{2}}^1 d y \int_{\frac{\pi}{6}}^{\arcsin y} f(x, y) d x$
B. $\int_{\frac{1}{2}}^1 d y \int_{\arcsin y}^{\frac{\pi}{2}} f(x, y) d x$
C. $\int_0^{\frac{1}{2}} d y \int_{\frac{\pi}{6}}^{\arcsin y} f(x, y) d x$
D. $\int_0^{\frac{1}{2}} d y \int_{\arcsin y}^{\frac{\pi}{2}} f(x, y) d x$