Example of a function $s\colon U\to \coprod_{P\in U} R_P$ in the structure sheaf

Question

Example of a function $s\colon U\to \coprod_{P\in U} R_P$ in the structure sheaf

I would like to see how the function actually works with an example.

I tried to make one, but I am not sure if it makes sense.

The function $s$ seems to take values prime ideals in $U$ and give us something in the localization.

Let $R=\mathbb{C}[x]$, then $\mathrm{spec}R = \{ \langle x-c \rangle, c\in \mathbb{C} \}$.

Let's take the prime ideal $P=\langle x-5\rangle$, the localization is $R_{P}=\{f/g: f,g\in R, g\notin P\}$

then $s$ is something like, for all $P\in U$, $s(P)=\frac{5}{x^2+3}\in R_P$ ?