# What is the integral of a constant?

The indefinite integral (with respect to $x$) of the constant function $C$ is $C x + D$, where $D$ is an arbitrary constant.

This question can be solved easily noting that

$\frac{d}{\mathrm{dx}} \left[C x + D\right] = C$

and aplying the fundamental theorem of calculus:

$\int C \mathrm{dx} = \int \frac{d}{\mathrm{dx}} \left[C x + D\right] \mathrm{dx} = C x + D$