Uniqueness Theorem. If F and G are antiderivatives of f on some interval Ii.e., F'(x) = G'(x) = f(x) for all x in I&n bsp;) then there is a constant C such that F(x) = G(x) + C for all x in I.

As a consequence of this theorem, we will usually add the constant C to an indefinite integral:

Discussion: