Use simulation with antithetic variables and find
$$\int_{-\infty}^\infty \int_0^\infty \sin(x+y)e^{-x^2+4x-y} \, dx \, dy.$$
so, my question and doubt is how struggle with the infinite limit ?
It is easy to me this problem $\int_0^1 e^x \, dx$ or similar, but do not know how the previous.
Help me please.