  In this paper, the $(p,q)$-derivative and the $(p,q)$-integration are
investigated. Two suitable polynomials bases for the $(p,q)$-derivative are
provided and various properties of these bases are given. As application, two
$(p,q)$-Taylor formulas for polynomials are given, the fundamental theorem of
$(p,q)$-calculus is included and the formula of $(p,q)$-integration by part is
proved.
