Consider the integral ${\displaystyle \underset{0}{\overset{1}{}}}{\displaystyle \underset{x^2}{\overset{1}{}}}\sqrt[\phantom{2}]{y}cos(y)dydx$

$(a)(2$ Points$)$ Sketch the region $of$ integration.

$(b)(4$ Points$)$ Change the order $of$ integration, and evaluate the new iterated integral.