$\displaystyle \int _ {- \frac{1} {\sqrt {2}}} ^ {0} {\left (\int _ {-x} ^ {\sqrt {1-x ^ {2}}} {y} dy \right) dx+ \int _ {0} ^ {\frac{1} {2}} {\left (\int _ {0} ^ {\sqrt {3} y} {y} dx \right) dy+ \int _ {\frac{1} {2}} ^ {1} {\left (\int _ {0} ^ {\sqrt {1-y ^ {2}}} {y} dx \right) dy}}}$ 의 값은?

• ①$\displaystyle \frac{1} {6} \left (\frac{1} {\sqrt {2}} + \frac{\sqrt {3}} {2} \right)$
• ②$\displaystyle \frac{1} {6} \left (\frac{1} {\sqrt {2}} - \frac{\sqrt {3}} {2} \right)$
• ③$\displaystyle \frac{1} {3} \left (\frac{1} {\sqrt {2}} - \frac{\sqrt {3}} {2} \right)$
• ④$\displaystyle \frac{1} {3} \left (\frac{1} {\sqrt {2}} + \frac{\sqrt {3}} {2} \right)$
• ⑤$\displaystyle \frac{1} {2}$