Answer
$\arctan x-x+1$
Work Step by Step
We need to integrate:
$y=\int (\dfrac{1}{x^2+1}-1) dx$
We use the differential trigonometric formula:
$\int \dfrac{1}{x^2+a^2}=\arctan (x/a)+C$
$y=\arctan x-x+c$
Take initial conditions: $y(0)=1$
Then $y(0)=\arctan (0)-0+c =1\implies c=1$
Thus, we have $y=\arctan x-x+1$
