设 $I_1=\iint_D \sin \left|\frac{x-y}{2}\right| \mathrm{d} x \mathrm{~d} y, I_2=\iint_D \sin \left(\frac{x-y}{2}\right)^2 \mathrm{~d} x \mathrm{~d} y, I_3=\iint_D \sin \left(\frac{x-y}{2}\right)^3 \mathrm{~d} x \mathrm{~d} y$, 其中 $D=$ $\left\{(x, y) \mid(x-1)^2+(y-1)^2 \leqslant 2\right\}$, 则
$\text{A.}$ $I_1 < I_2 < I_3$
$\text{B.}$ $I_2 < I_3 < I_1$
$\text{C.}$ $I_3 < I_1 < I_2$
$\text{D.}$ $I_3 < I_2 < I_1$