$\displaystyle \int _ {0} ^ {\frac{\sqrt {\pi}} {2}} \int _ {y} ^ {\frac{\sqrt {\pi}} {2}} 2 \cos \left (x^ {2} + \frac{\pi} {4} \right) d x d y$ 의 값은?

• ①$\displaystyle \frac{\sqrt {2} -1} {2}$
• ②$\displaystyle \frac{\sqrt {3} -1} {2}$
• ③$\displaystyle \frac{\sqrt {3} - \sqrt {2}} {2}$
• ④$\displaystyle \frac{2- \sqrt {2}} {2}$
• ⑤$\displaystyle \frac{2- \sqrt {3}} {2}$