The function y = f(x) is the solution of the differential equation
$$\frac{\text{d}y}{\text{d}x} + \frac{xy}{x^2 - 1} = \frac{x^4 + 2x}{\sqrt {1 - x^2}}$$
in (−1, 1) satisfying f(0) = 0. Then
$$\int_{-{\frac{\sqrt 3}{2}}}^{\frac{\sqrt 3}{2}} f(x) dx $$ is

A

$$\frac{\pi}{3} - \frac{\sqrt 3}{2}$$

B

$$\frac{\pi}{3} - \frac{\sqrt 3}{4}$$

C

$$\frac{\pi}{6} - \frac{\sqrt 3}{4}$$

D

$$\frac{\pi}{6} - \frac{\sqrt 3}{2}$$