教えてください

δ関数を含む積分
①∫[-∞,∞] {(1+sin(x))/(1+sin(x)+(2x/π)^2)}･δ(x-π/2) dx

②exp(-a|x|) = ∫[-∞,∞] exp(ikx)･g(k) dk
を満たすg(k) (i=√(-1))