Answer
$\tan^{-1} (y-1) +C$
Work Step by Step
We integrate the integral as follows:
$I=\int \dfrac{dy}{y^2-2y+2}=\int \dfrac{dy}{(y-1)^2+1}$
Using the Substitution Method:
$y-1=u \implies dy=du$
Now, $I=\int \dfrac{du}{u^2+1} \\=\tan^{-1} (u) +C \\=\tan^{-1} (y-1) +C$
