Consider \(f(x) = x^2/3\) over \(R\) = [-1,2]. Then, for \(-1 \le x \le 2\text{,}\)
\begin{equation*}
F(x) = \int_{-1}^x u^2/3 du = x^3/9 + 1/9.
\end{equation*}
Notice, \(F(-1) = 0\) since nothing has yet been accumulated over values smaller than -1 and \(F(2) = 1\) since by that time everything has been accumulated. In summary: Table 5.3.9. Continuous Distribution Function Example
| X | F(x) |
| \(x \lt -1\) | 0 |
| \(-1 \le x \lt 2\) | \(x^3/9 + 1/9\) |
| \(2 \le x\) | 1 |