places of function field and closed point of a scheme

Question

Given an integral scheme $X$, let $K(X)=\mathrm{Frac}(R)$ be its function field, where $\mathrm{Spec}(R)$ is some non-empty open affine subscheme of $X$. Take the maximal ideal $P$ of some DVR of $K(X)$ (i.e. a place $P$). How can one associate a closed point of $X$? Does it exist a bijection between closed points of $X$ and places of $K(X)$?