The key concept in integral calculus is integration, a procedure that involves computing a special kind of limit sums called the definite integral. During the eighteenth century, integrals were considered simply as antiderivatives. That is there were no underpinnings for the concept of an integral until Cauchy formulated the definition of integral in 1823. The formulation was later completed by Friedrich Riemann. The knowledge of integrals found applications such as computing area, volume, arc length, surface area, work, hydrostatic force, centroids of planar regions, and applications to business, economics, and life sciences.