Find the area of the region bounded by the following equations in the range of x from -1 to 1.
The larger root of x^2 + x - 1 = -1/2 + sqrt(5)/2 ~ 0.618 (https://www.mathsisfun.com/quadratic-equation-solver.html).
The area between the curves will be equal to:
(Area between curve and x-axis for -3x^3 +3x + 2 in range -1 to 1) + (Area between curve and x-axis for x^2 +x - 1 in range -1 to 0.618) - (Area between curve and x-axis for x^2 +x - 1 in range 0.618 to 1)
Use the definite integral to get all three of these areas. Simply take absolute value when integral is negative.
For this, we use the following calculator:
https://www.symbolab.com/solver/definite-integral-calculator
We get the following:
Area bounded by the equations = 4 + 1.51503 - 0.18169 = 5.33 units squared.