Differential Equations: JEE Main 2022 Mathematics question

Let the solution curve $y=f(x)$ of the differential equation $\frac{d y}{d x}+\frac{x y}{x^{2}-1}=\frac{x^{4}+2 x}{\sqrt{1-x^{2}}}$, $x\in(-1,1)$ pass through the origin. Then $\int\limits_{-\frac{\sqrt{3}}{2}}^{\frac{\sqrt{3}}{2}} f(x) d x$ is equal to