Let $$[x]$$ denote the greatest integer $$\leq x$$. Consider the function $$f(x) = \max\{x^2, 1 + [x]\}$$. Then the value of the integral $$\int_0^2 f(x) dx$$ is:

A

$$\frac{5+4\sqrt{2}}{3}$$

B

$$\frac{8+4\sqrt{2}}{3}$$

C

$$\frac{1+5\sqrt{2}}{3}$$

D

$$\frac{4+5\sqrt{2}}{3}$$