  In this article, we investigate the asymptotic behaviour of the spatial
integral of the solution to the parabolic Anderson model with time independent
noise in dimension $d\geq 1$, as the domain of the integral becomes large. We
consider 3 cases: (a) the case when the noise has an integrable covariance
function; (b) the case when the covariance of the noise is given by the Riesz
kernel; (c) the case of the rough noise, i.e. fractional noise with index $H
\in (\frac{1}{4},\frac{1}{2})$ in dimension $d=1$. In each case, we identify
the order of magnitude of the variance of the spatial integral, we prove a
quantitative central limit theorem for the normalized spatial integral by
estimating its total variation distance to a standard normal distribution, and
we give the corresponding functional limit result.
