JEE Math Practice Question

$$\mathop {\lim }\limits_{x \to {\pi \over 2}} \left( {{1 \over {{{\left( {x - {\pi \over 2}} \right)}^2}}}\int\limits_{{x^3}}^{{{\left( {{\pi \over 2}} \right)}^3}} {\cos \left( {{t^{{1 \over 3}}}} \right)dt} } \right)$$ is equal to

1. A.$$\frac{3 \pi^2}{4}$$
2. B.$$\frac{3 \pi^2}{8}$$
3. C.$$\frac{3 \pi}{4}$$
4. D.$$\frac{3 \pi}{8}$$