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