The equation of the curve whose slope is y−1x2+x and which passes through the point (1,0) is

∫1x2+xdx=∫dyy−1⇒∫1x(x+1)dx=∫dyy−1⇒log⁡x−log⁡(x+1)=log⁡(y−1)+log⁡c⇒xx+1=c(y−1) pass (1,0)⇒c=-1/2⇒xx+1=−1/2(y−1)⇒xy+x+y−1=0