Should I add a constant $C$ in this step of doing an integral?

Question

Should I add a constant $C$ in this step?

$$\begin{align*} \int \left(\sec^2x \, dx - \sec x \tan x \, dx\right) &= \tan x - \int \sec x \tan x \, dx\\\\ \int \left(\sec^2x \, dx - \sec x \tan x \, dx\right) &= \tan x + C - \int \sec x \tan x \, dx \end{align*}$$

Answer 1

It is okay not to add one at this step: the remaining integral on the right hand side already creates an arbitrary constant of integration... and the sum of two arbitrary constants is just another arbitrary constant!

Answer 2

You dont really need to add one, just add one at the very end