Let $$f'(x) = \frac{192x^3}{2 + \sin^4 \pi x}$$ for all $$x \in R$$ with $$f\left(\frac{1}{2}\right) = 0$$. If $$m \leq \int_{\frac{1}{2}}^{1} f(x) dx \leq M,$$ then the possible values of m and M are

A

$$m = 13, M = 24$$

B

$$m = \frac{1}{4}, M = \frac{1}{2}$$

C

$$m = -11, M = 0$$

D

$$m = 1, M = 12$$