I'm confused. Can't see the LaTeX, don't know what a,b,c are.
Just note that the derivative of a constant function C is zero: and
Therefore could equal or for any constant C. Because for a given anti-derivative, we can shift that function up or down, and it doesn't change the value of at that x-coordinate. The same applies to vector-valued functions, where C is an arbitrary constant vector
Edit: I see the solution now, thanks