  In order to study integral points of bounded log-anticanonical height on weak
del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative
example, we consider a quartic del Pezzo surface of singularity type
$\mathbf{A}_1+\mathbf{A}_3$ and prove an analogue of Manin's conjecture for
integral points with respect to its singularities and its lines.
