A cycle path in a nature reserve has the profile $y = (x - 1)(x - 2)(x - 3)$ for $1 \le x \le 3$, with $x$ in kilometres and $y$ in kilometres, as in the figure. The path crosses a reference line $y = 0$ at three points. The reserve wants the total area between the profile and the reference line. What is this area, in square kilometres?

Fig. 1: The blue curve y = (x - 1)(x - 2)(x - 3) from x = 0.6 to x = 3.4. It crosses the x-axis at 1, 2 and 3. Between 1 and 2 the curve is above the axis in a small hump shaded green. Between 2 and 3 it is below the axis in a small dip of the same size, shaded red.