  We consider shape optimization problems for general integral functionals of
the calculus of variations, defined on a domain $\Omega$ that varies over all
subdomains of a given bounded domain $D$ of ${\bf R}^d$. We show in a rather
elementary way the existence of a solution that is in general a quasi open set.
Under very mild conditions we show that the optimal domain is actually open and
with finite perimeter. Some counterexamples show that in general this does not
occur.
