이중적분 $\displaystyle \int _ {0} ^ {\pi} \int _ {- \sin \frac{x} {2}} ^ {\sin x} \frac{\left (1- | y | \right) \left (1-y^ {1 / 3} \right)} {\sqrt{1-y^ {2}}} d y d x$ 의

값은?

• ①$\displaystyle \frac{1} {2} \left (8-5 \pi + \pi ^ {2} \right)$
• ②$\displaystyle \frac{1} {2} \left (9-5 \pi + \pi ^ {2} \right)$
• ③$\displaystyle \frac{1} {2} \left (7-4 \pi + \pi ^ {2} \right)$
• ④$\displaystyle \frac{1} {2} \left (8-4 \pi + \pi ^ {2} \right)$
• ⑤$\displaystyle \frac{1} {2} \left (9-3 \pi + \pi ^ {2} \right)$