Evaluate $\displaystyle{\int_{-\pi}^{\pi} f(x)\, dx}$, where $$f(x) = \begin{cases} 6 x^{2}, & -\pi \leq x < 0 \\ 3 \sin(x), & 0 \leq x \leq \pi. \end{cases}$$

$\displaystyle{\int_{-\pi}^{\pi} f(x)\, dx}$ =