On account of integral representations regarded as the basic theory of complex analysis and a significant tool for solving boundary value problems, integral representations for a class of broader generalized poly-analytic functions are proposed and established. By using decomposition theorem and Cauchy-Pompeiu formula of generalizedβ-analytic functions, together with matrix transformation and the theory of Fredholm integral equations, various integral representations are investigated. Various integral representations including with shift and without shift are obtained, the extension theorem of higher order poly- Cauchy type integral is proved, and the application in solving a class of Riemann jump problems is also provided. Several types of integral representations for a class of generalized poly-analytic function are established, which extend and generalize the integral representation theory of analytic functions, especially poly-analytic functions, and also provide theoretical support for the research on boundary value problems and singular integral operators related to β-analytic functions in the future.