Given a real function f, any function ϕ‎ such that ϕ‎′(x) = f(x), for all x (in the domain of f), is an antiderivative of f. If ϕ‎₁ and ϕ‎₂ are both antiderivatives of a continuous function f, defined on an interval, then ϕ‎₁(x) and ϕ‎₂(x) differ by a constant. In that case, the notation

may be used for an antiderivative of f, with the understanding that an arbitrary constant can be added to any antiderivative. Thus,

where c is an arbitrary constant, is an expression that gives all the antiderivatives of f.