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We prove that if $R$ is $F$-injective in characteristic $p>0$ or Du Bois in characteristic $0$, then the truncated dualizing complex $\\tau_{>-j}\\omega_R^\\bullet$ is quasi-isomorphic to a complex of $k$-vector spaces. As a consequence, $F$-injective or Du Bois singularities with isolated non-Cohen-Macaulay locus are Buchsbaum. 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