Let $f:(-1,1) \to R$ be a continuous function . If $\int\limits_0^{\sin x }f(t)dt =\large\frac{\sqrt 3}{2}$$x$ , then $f\bigg(\large\frac{\sqrt 3}{2} \bigg)$ is equal to

Question

$\begin{array}{1 1} \frac{\sqrt 3}{2} \\ \sqrt 3 \\ \sqrt{\frac{3}{2}} \\\frac{1}{2} \end{array}$