Area of region bounded by two curves (Calculus)

Functions y=x^2, ad y=-x^2, between -1, and 1. Please show all work. Thank you.

Area of a curve is the integral of the difference of the top curve and the bottom curve: Area = Integral from -1 to 1 ((x^2 - (-x^2)) dx)

Simplify: Area = Integral from -1 to 1 ((x^2 + x^2) dx)

Simplify: Area = Integral from -1 to 1 (2x^2 dx)

Integrate: Area = (2/3)x^3 from -1 to 1

Substitute 1 for x and -1 for x then take the difference: Area = (2/3)(1)^3 - (2/3)(-1)^3

Simplify: (2/3) - (-2/3)

Simplify: (2/3) + (2/3)

Simplify: 4/3

(1/2) dV = π (x^2 - (-x^2)) dx = π 2x^2 dx

dV = 4π x^2 dx

V = 4π ∫ {0, 1} x^2 dx = 4π/3 x^3

Evaluating: 4π/3 [1^3 - 0^3] = 4π/3

by symmetry 4* (1^3/3) = 4/3