firstly, if I want to find the points on intersection on this graph between the curve and line, I'd set thier y values equal to each other.

$\displaystyle y = x^3 $

$\displaystyle y = -x+2 $

$\displaystyle x^3 = -x +2 $

$\displaystyle x^3 +x -2 = 0 $

how do I solve that?

or do I not need these points when working out the area ?