Primitive of Constant

Theorem
Let $c$ be a constant.
 * $\displaystyle \int c \ \mathrm dx = c x + C$ where $C$ is an arbitrary constant.

Proof
Let $\displaystyle F \left({x}\right) = \int c \ \mathrm dx$

Then from the definition of indefinite integral:
 * $F' \left({x}\right) = c$

From Derivative of Function of Constant Multiple:
 * $D_x \left({c x}\right) = c$

From Primitives which Differ by Constant:
 * $D_x \left({c x + C}\right) = c$

Hence the result.