What is the Purpose of U Substitution in Solving Integrals?

[bmed90]

Homework Statement

the integral of 1/(1-y)dy

Homework Equations

The Attempt at a Solution

ln|1-y|+C

however I believe you use u substitution as 1-y=U? Why is this so?

 

[LeonhardEuler]

You lost a minus sign in your solution. Making a substitution would work because the integral would reduce to
$$\int{-\frac{1}{u}du}$$
which is well known, but this example is simple enough that you could solve it just by looking at it.