Hello everyone. Our professor discussed this particular problem the other day:

At any point (x,y) on a curve, d2y/dx2 = 1 - x^2. The equation of the tangent line to the curve at (1,1) is y = -x + 2. Find the equation of the curve.

I have notes on the solution but I’m stuck. I don’t understand why dy/dx equals to -1. Can someone please lead me in the right direction? Attached is the picture of my lecture notes.

Thank you very much!