In calculus, the indefinite integral of a given function (i.e., the set of all antiderivatives of the function) is only defined up to an additive constant, the constant of integration. This constant expresses an ambiguity inherent in the construction of antiderivatives. If a function is defined on an interval and is an antiderivative of , then the set of all antiderivatives of is given by the functions , where C is an arbitrary constant. The constant of integration is sometimes omitted in lists of integrals for simplicity.