Application of Integration

Consider the functions defined implicitly by the equation y3 − 3y + x = 0 on various intervals in the real line. If x ∈ (-∞, -2) ∪ (2, ∞), the equation implicitly defines a unique real valued differentiable function y = f(x).
If x ∈(-2, 2), the equation implicitly defines a unique real valued differentiable function y = g(x) satisfying g(0) = 0.

The area of the region bounded by the curves y = f(x), the x-axis, and the lines x = a and x = b, where -∞ < a < b < -2, is