antiderivative x-axis limit Riemann sum area integration function graph algebra derivative integral areas
Integral calculus is the study of the definitions, properties, and applications of two related concepts, the indefinite integral and the definite integral. The process of finding the value of an integral is called integration. The indefinite integral, also known as the antiderivative, is the inverse operation to the derivative. F is an indefinite integral of f when f is a derivative of F.  (This use of lower- and upper-case letters for a function and its indefinite integral is common in calculus.) The definite integral inputs a function and outputs a number, which gives the algebraic sum of areas between the graph of the input and the x-axis. The technical definition of the definite integral involves the limit of a sum of areas of rectangles, called a Riemann sum.
