This work's content has been built on the material created in the first two companion papers on the very newly proposed method named "Separate Node Ascending Derivatives Expansion (SNADE) for Univariate Functions". Those four companion papers are to appear in this proceedings. This work focuses on the univariate numerical integration of a given univariate function by using SNADE. Almost trivial polynomial integration has been empowered by integrating the SNADE remainder integral. To this end the integral representation of the SNADE remainder has been reformulated in unit hypercubic format. The factor arising in the integrand to multiply the target function's relevant derivative has been separated to appropriate pieces to get weighted integrals under strictly positive multivariate weight functions. Paper emphasizes totally onconceptuality and formulation. Hence we do not present any illustrative implementations here.