# probability – Find the mean of \$Y=frac{1}{A}(e^{A}-1)\$ where \$Asim N(0,sigma^2)\$

A sub-question of an exercise from my probability class is as follows:

Let $$Asim N(0,sigma^2)$$ and $$X(t)=e^{At}$$. Find the mean of $$Y=int_0^1X(t)dt$$.

I figured that we have $$Y=frac{1}{A}(e^{A}-1)cdotunicode{x1D7D9}_{{Aneq 0}}$$ so that the mean is equal to

begin{align} mathbb{E}(Y) & = frac{1}{sqrt{2pisigma^2}}int_{-infty}^inftyfrac{e^x-1}{x}exp{(-frac{x^2}{2sigma^2})}dx. end{align}

I do, however, have not the slightest idea as to how I should proceed from here. I am doubting whether I am even approaching the question in the right way.