Assume that $n(t)$ is a White Gaussian Noise (WGN) process with $E[n(t)]=0$, $E[n(t)^2]=\sigma^2$ and $x(t)$ a deterministic function defined in $[0,T]$. How can I compute from first principles the variance of $g(T)$ defined as
$g(T)=\int_0^Tx(t)n(t)dt.$
Any references to elementary textbooks on stochastic processes are also welcome.