For Choquet integrals, two different frameworks are typically used. The first, introduced by Schmeidler, uses a space of bounded measurable functions, the second, studied by Zhou, uses a Stone vector lattice. In the present paper, the authors find a unified treatment. They extend Choquet integral representations to general, not necessarily monotone, set functions, and they extend the Daniell-Stone Theorem to the comonotonic additive case.