Question about the constant that occures after differentiation/integration

Hi!

I have a question about something I find a bit peculiar. The textbook of my math-course is a bit inconistent in the use of the constant (here ) that comes from differentiating an expression.

I have an expression that has been differentiated, and it looks like this:

Sometimes this kind of expression is used to calculate further, but other times it is manipulated into this:

My question is this:

Can I always perfrom this manipulation, or is it just in certain circumstances? I know the constant is a constant that can be changed if it is only affected by other constants (like in this situation), but the whole thing is very confusing...

Any clarifying help will be greatly appreciated!

Thomas