  We estimate the intrinsic neutral gas density in Damped Lyman Alpha systems
($\Omega_{HI}^{(DLA)}$) in the redshift range $ 2.2 \lesssim z \lesssim 5$ from
the DLA SDSS DR_3 sample of optically selected quasars. We take into account
self-consistently the obscuration on background quasars due to the dust present
in Damped Lyman Alpha systems. We model the column density and redshift
distribution of these systems by using both a non-parametric and a parametric
approach. Under conservative assumptions on the dust content of Damped Lyman
$\alpha$ systems, we show that selection effects lead to underestimating the
intrinsic neutral gas density by at least $15\%$ with respect to the observed
neutral gas density. Over the redshift range $[2.2;5.5]$ we find
$\Omega_{HI}^{(DLA)}=0.97^{+0.08+0.28}_{-0.06-0.15} \cdot 10^{-3}$, where the
first set of error bars gives the $1\sigma$ random errors and the second set
gives the modeling uncertainty dependent on the fraction of metals in dust -
from 0\% to 50\%. This value compares with
$\Omega_{HI}^{(DLA)}=0.82^{+0.05}_{-0.05}$ ($1\sigma$ error bars), which is
obtained when no correction for dust is introduced. In the model with half of
the metals mass in dust we cannot constraint $\Omega_{HI}^{(DLA)}$ at a
confidence level higher than $90\%$. In this case there is indeed a probability
of about $10\%$ that the intrinsic column density distribution of DLA systems
is a power law $f(N_{HI}) \propto 1/N_{HI}^{~1.95}$. In contrast, with $25 \%$
of the metals in dust - the most realistic estimate - a power law is ruled out
at $99.5\%$ of confidence level.
