Example 6.3.2. Basic Continuous Uniform.
On \(R = [1,2 \pi]\text{,}\)
\begin{equation*}
f(x) = \frac{1}{2 \pi - 1}.
\end{equation*}
Then, if you want to compute something like \(P(2 < X < 4.5)\) integrate
\begin{equation*}
P(2 < X < 4.5) = \int_2^{4.5} \frac{1}{2 \pi -1} dx = \frac{2.5}{2 \pi - 1}
\end{equation*}