Integral
![A definite integral of a function can be represented as the signed area of the region bounded by its graph.](/Images/godic/202501/20/Integral_example.svg4046.png")
![Approximations to integral of √x from 0 to 1, with 5 ■ (yellow) right endpoint partitions and 12 ■ (green) left endpoint partitions](/Images/godic/202501/20/Integral_approximations.svg4046.png")
![Darboux sumsDarboux upper sums of the function y = x2Darboux lower sums of the function y = x2](/Images/godic/202501/20/Riemann_Integration_and_Darboux_Upper_Sums4046.gif")
![Lower Darboux sum example](/Images/godic/202501/20/Riemann_Integration_and_Darboux_Lower_Sums4047.gif")
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data. Integration is one of the two main operations of calculus, with its inverse, differentiation, being the other. Given a function f of a real variable x and an interval [a, b] of the real line, the definite integral