Integral calculus is the study of integration and methods for evaluating integrals. Integrals come in two kinds, definite and indefinite. The definite integral of a function, interpreted geometrically, corresponds to the area under the curve of the function between any two limits. Thus, it has a definite value depending on the limits chosen, The indefinite integral of a function is the inverse of the derivative of that function. That is, integrating (finding the integral) undoes differentiating (finding the derivative f'(x)). Integrating the derivative of a function returns the original function.
Science EncyclopediaScience & Philosophy: Calcium Sulfate to Categorical imperativeCalculus - History, Differential Calculus, Integral Calculus, Indefinite Integral, Definite Integral