  We prove local boundedness of local minimizers of scalar integral functionals
$\int_\Omega f(x,\nabla u(x))\,dx$, $\Omega\subset\mathbb R^n$ where the
integrand satisfies $(p,q)$-growth of the form \begin{equation*} |z|^p\lesssim
f(x,z)\lesssim |z|^q+1 \end{equation*} under the optimal relation
$\frac1p-\frac1q\leq \frac1{n-1}$.
