Two solutions for the same integral question, which approach is correct/better to solve?

Question

I solved the following integral by 'u' substitution:

$\int \frac{y}{y+1}dy$

$ u = y + 1$

$ y = u - 1$

$=\int \frac{\left(u-1\right)}{u}du$

After finally separating nominator and denominator, and putting values of u, we get:

$=y+1-\ln \left|y+1\right|$

But my instructor does it this way(she basically divided the denominator with nominator):

$\int \left(1\:-\:\frac{1}{y+1}\right)dy$

which yields the following answer:

$=y-\ln \left|y+1\right|$

Which is slightly different from the answer yielded by 'u' substitution.

I wanted to know which method or approach is correct or better to solves such types of integral question?

Answer 1

Primitive functions are determined only up to an additive constant. Both answers are equally correct...yet both are missing the addition of a constant.