Let $$f : R \rightarrow R$$ be given by $$f(x) = (x - 1)(x - 2)(x - 5).$$ Define
$$F(x) = \int_{0}^{x} f(t) dt, x > 0.$$
Then which of the following options is/are correct?

A

F has local minimum at x = 1

B

F has local maximum at x = 2

C

F has two local maxima and one local minimum in $$(0, \infty)$$

D

$$F(x) \neq 0$$ for all $$x \in (0,5)$$