## Quick Reference

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 *φ*_{1} and *φ*_{2} are both antiderivatives of a continuous function f, then *φ*_{1}(*x*) and *φ*_{2}(*x*) differ by a constant. In that case, the notation

*∫**f*(*x*) *dx*

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

*∫**f*(*x*) *dx* + *c*,

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

*Subjects:*
Mathematics.