A function F (x) is an h-antiderivative of f (x) if D h F (x) = f (x). The h-integral is denoted by ∫ ∫ f ( x ) d h x . If a and b differ by an integer multiple of h then the definite integral ∫ ∫ a b f ( x ) d h x is given by a Riemann sum of f (x) on the interval [ a, b ], partitioned into sub-intervals of equal width h. The motivation of h-integral comes from the Riemann sum of f(x). Following the idea of the motivation of classical integrals, some of the properties of classical integrals hold in h-integral. This notion has broad applications in numerical analysis, and especially finite difference calculus.