Primitives which Differ by Constant/Corollary
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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.
$\blacksquare$