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

A

$$\int_{a}^{b} \frac{x}{3\left((f(x))^2 - 1\right)}dx + bf(b) - af(a)$$

B

$$-\int_{a}^{b} \frac{x}{3\left((f(x))^2 - 1\right)}dx + bf(b) - af(a)$$

C

$$\int_{a}^{b} \frac{x}{3\left((f(x))^2 - 1\right)}dx - bf(b) + af(a)$$

D

$$-\int_{a}^{b} \frac{x}{3\left((f(x))^2 - 1\right)}dx - bf(b) + af(a)$$