Integral of 2^(-x^2) from 1 to infinity.
Well, "derive" is not that great a word for the process. I wanted to invent a structure that was easily integrated. The $\displaystyle x^{2}$ in the exponent suggested another 'x' out front would be good - thinking about the simple substitution $\displaystyle u = x^{2}$. After that, it was just a bit of thought to determine EXACTLY why the problem suggested the Domain $\displaystyle [1,\infty)$ rather than $\displaystyle [0,\infty)$.
That's about it. You just have to think it through and figure it out.