In calculus, the indefinite integral of a given function (i.e., the set of all antiderivatives of the function) on a connected domain 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.