Area = 10 2/3
It might help to graph the two equations. y=-x^2 is a downward opening parabola with vertex = origin = (0,0) = the maximum point. y=-4 r is a flat horizontal line, with zero slope, intersecting the y axis at (0,-4)
the two graphs intersect at (-2,-4) and (2,4) which gives the limits of evaluation, x=-2 and x=2
Area = the integral of (-x^2 -(-4)) = 4-x^2
= 4x -x^3/3 evaluated from -2 to 2
= 4(2) - (2)^3/3 - [4(-2) - (-2)^3/3]
= 8 -8/3 -[-8 + 8/3]
= (24-8)/3 + 8-8/3
= 16/3 + 16/3
= 32/3
= 10 2/3
