Antiderivative Definite Integral And Average Value

Let the function $$f$$ be defined by $$f(x) = 4x - 1$$. Consider the following statements.

I. An antiderivative of $$f$$ is $$2x^2 - x$$.
II. $$\int_0^2 (4x - 1)\,dx = 6$$.
III. The average value of $$f$$ on the interval $$[0, 2]$$ is 3.

Which of the statements is/are correct?