JEE Math Practice Question

Let f be a differentiable function in $$\left( {0,{\pi \over 2}} \right)$$. If $$\int\limits_{\cos x}^1 {{t^2}\,f(t)dt = {{\sin }^3}x + \cos x} $$, then $${1 \over {\sqrt 3 }}f'\left( {{1 \over {\sqrt 3 }}} \right)$$ is equal to

1. A.$$6 - 9\sqrt 2 $$
2. B.$$6 - {9 \over {\sqrt 2 }}$$
3. C.$${9 \over 2} - 6\sqrt 2 $$
4. D.$${9 \over {\sqrt 2 }} - 6$$