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In this paper we introduce the moduli stack $\widetilde{\mathscr{M}}_{g,n}$of $n$-marked stable at most cuspidal curves of genus $g$ and we use it todetermine the integral Chow ring of $\overline{\mathscr{M}}_{2,1}$. Along theway, we also determine the integral Chow ring of$\overline{\mathscr{M}}_{1,2}$.

Stable cuspidal curves and the integral Chow ring of $\overline{\mathscr{M}}_{2,1}$