Primitives which Differ by Constant/Corollary

Theorem

Let $f$ be an integrable function on the closed interval $\closedint a b$.

Then there exist an uncountable number of primitives for $f$ on $\closedint a b$.

Proof

By definition of integrable function, $f$ has a primitive $F$ (at least one).

By Primitives which Differ by Constant, for every real number $C$, if $\map F x$ is a primitive of $f$, then so is $\map G x$ where:

$\forall x \in \closedint a b: \map G x = \map F x + c$

The Real Numbers are Uncountable.

Hence the result.

$\blacksquare$