Evaluate $\displaystyle{\int_0^2 f(x)\, dx}$, where $$f(x) = \begin{cases} 3 x^{5}, & 0 \leq x < 1 \\ 6 x^{4}, & 1 \leq x \leq 2. \end{cases}$$

$\displaystyle{\int_0^2 f(x)\, dx}$ =