Integrate : $\int \limits_0^{\large\frac{\pi}{2}} max ^m \{ \sin x , \cos x \} dx$

Question

$$\begin {array} {1 1} (a)\;2+\sqrt 2 \\ (b)\;1+\sqrt 2 \\ (c)\;\sqrt 2 \\ (d)\;2 \sqrt 2 \end {array}$$