Primitive of Constant

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

Proof
Let:
 * $\displaystyle \map F x = \int c \rd x$

From the definition of primitive:
 * $\map {F'} x = c$

From Derivative of Function of Constant Multiple:
 * $\map {D_x} {c x} = c$

From Primitives which Differ by Constant:
 * $\map {D_x} {c x + C} = c$

Hence the result.