How to determine the area bounded by the curves?

Question

Determine the area bounded by the curves y = e^x, y = x² - 1, x = -1, and x = 1.

Answer 1

integral of e^2 evaluated from -1 to 1 is

e - 1/e

add to that the area below the x axis and the parabola x^2-1

change the sign of the integral of x^2-1 evaluated between 0 and 1

then double it

x^3/3-x evaluated from 0 to 1 is

1/3-1 = -2/3, change its sign to 2/3

double it to get 4/3

total area between the two curves is

e - 1/e + 4/3