If dy/dx = -x^2 +2x-1 and the point (1,5/3) belongs to the curve, find the equation for y?

Answer 1

Simply integrate term by term to get y = -(x³/3)+x²-x+C

Then plug in the point: 5/3 = -(1/3)+1-1+C so that C = 2 and your answer is

y = -(x³/3) + x² - x + 2