  Let $p\colon \mathcal{A} \to G$ be a saturated Fell bundle over a locally
compact, Hausdorff, second countable, {\'e}tale groupoid~$G$, and let
$\mathrm{C}^*(G;\mathcal{A})$ denote its full $\mathrm{C}^*$-algebra. We prove
an integration-disintegration theorem for KMS states on
$\mathrm{C}^*(G;\mathcal{A})$ by establishing a one-to-one correspondence
between such states and fields of measurable states on the
$\mathrm{C}^*$-algebras of the Fell bundles over the isotropy groups. This
correspondence is established for certain states on
$\mathrm{C}^*(G;\mathcal{A})$ also. While proving this main result, we
construct an induction $\mathrm{C}^*$-correspondence
between~$\mathrm{C}^*(G;\mathcal{A})$ and the $\mathrm{C}^*$-algebra of an
isotropy Fell bundle. We demonstrate our results through many examples such as
groupoid crossed products, twisted groupoid crossed products, $G$-spaces and
matrix algebras~$\mathrm{M}_n(\mathrm{C}(X))\otimes A$. While studying the
matrix algebra~$\mathrm{M}_n(\mathrm{C}(X))$, we propose a groupoid model for
it. While demonstrating our main result for this groupoid model, we provide a
solution to the Radon--Nikodym problem for the groupoid used in this model.
