This problem has been worked out for me, but I am confused about what exactly is going on in it.

Problem: Find the indefinite integral.

∫-1/sqrt(1-(2t-1)^2) dt

Step 1: Let u= 2t -1

Step 2: du= 2 dt

Step 3: ∫ -1/sqrt(1-(2t-1)^2) dt

= -1/2 ∫ 2/sqrt(1-(2t-1)^2) dt

Step 4: = -1/2 arcsin(2t-1) + C

The main thing I don't understand is where the

-1/2 before the ∫ sign is coming from in Step 3, and why the -1 changed to a 2 in the part after the ∫ sign. If anyone could explain to me what is going on in this problem I would greatly appreciate it. Thanks.