Find $int_0^{frac{pi}{2}} e^{-a(sin(x)+cos(x))} , dx$ and/or $int_0^{frac{pi}{2}} e^{-a(sin(x)+cos(x))} sin(cos(x)) , dx$

While trying to solve a certain integral I was left with these rather silly integral.

$$int_0^{frac{pi}{2}} e^{-a(sin(x)+cos(x))} , dx$$
$$int_0^{frac{pi}{2}} e^{-a(sin(x)+cos(x))} sin(cos(x)) , dx$$

Any headway on these problems would be greatly appreciated!