$$\lim_{x \to \frac{\pi}{2}} \left(\frac{1}{(x - \frac{\pi}{2})^2} \int_{x^3}^{(\frac{\pi}{2})^3} \cos\left(\frac{1}{t^3}\right) dt\right)$$ is equal to

A

$$\frac{3\pi}{8}$$

B

$$\frac{3\pi^2}{4}$$

C

$$\frac{3\pi^2}{8}$$

D

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