  Consider the parabolic Anderson model
$\partial_tu=\frac{1}{2}\partial_x^2u+u\, \eta$ on the interval $[0, L]$ with
Neumann, Dirichlet or periodic boundary conditions, driven by space-time white
noise $\eta$. Using Malliavin-Stein method, we establish the central limit
theorem for the fluctuation of the spatial integral $\int_0^Lu(t\,, x)\,
\mathrm{d} x$ as $L$ tends to infinity, where the limiting Gaussian
distribution is independent of the choice of the boundary conditions and
coincides with the Gaussian fluctuation for the spatial average of parabolic
Anderson model on the whole space $\mathbb{R}$.
