Integral question and answer confirmation please!

I am suppose to evaluate the indefinite integral of

dx / square root of (1 - x^2 +2x)..

I first broke down 1-2^x + 2x into 2-(x-1)^2

I then took the antiderivative of dx/(2-(x-1)^2) and came up with the answer of [sin^-1(x-1) / 2] + C

Can someone please tell me if this is correct, or what i can do to make it right? I took the derivavtive and it seems i might have made a small error somewhere in finding the antiderivative but im not soo sure where...

Also, if someone can help me solve this question, thatd be great, thanks!!(Rofl)

Compute the integral from -1 ->3 of the square root of (6-2x^2 +4x)dx .

I can't find the antiderivative of this function...and substitution doesnt seem to work...