where did that come from?

To make it less confusing, first know that: \(1-y = -(y-1)\).

Then, using the property of absolute value function, we have: \(|-x| = |x|\)

It is supposed to be \(-\ln|1-y| + C\), however, \(-\ln|1-y| = -\ln|-(y-1)| = -\ln|y-1|\).

Both \(-\ln|1-y| + C\) and \(-\ln|y-1| + C\) are correct answers.

The straight lines around 1-y mean "take the absolute value of".  The absolute value of 1-y is the same as that of y-1, so, as Max noted, ln(|y-1|) is the same as ln(|1-y|).