Constant of integration

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 ${\displaystyle f(x)}$ is defined on an interval and ${\displaystyle F(x)}$ is an antiderivative of ${\displaystyle f(x)}$, then the set of all antiderivatives of ${\displaystyle f(x)}$ is given by the functions ${\displaystyle F(x)+C}$, where C is an arbitrary constant (meaning that any value for C makes ${\displaystyle F(x)+C}$ a valid antiderivative). The constant of integration is sometimes omitted in lists of integrals for simplicity.

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