Let $X$ and $Y$ be integral schemes and $f : X \to Y$ a morphism. Let $X_{\eta'}$ be the fiber of $f$ over the generic point $\eta'$ of $Y$, i.e. the base change $X_{(K)} = X \times_Y K$ where $K = \mathrm{Spec}(\mathscr{O}_{Y,\eta'})$. Why (when) is $X_{\eta'}$ integral?
The context of this question is the proof of (Stacks, 29.20.2), see the third paragraph from the end. There $X$ and $Y$ are locally Noetherian, and $f$ is proper and locally of finite type, but I don't know if this is necessary here.
If $X,Y$ are affine (always check this first!), the question becomes: Let $A \to B$ be a homomorphism of integral domains, is then $B \otimes_A Q(A)$ an integral domain? Well, it is isomorphic to the localization $(A \setminus \{0\})^{-1} B$. Localizations of integral domains are either $0$ or again integral domains. The localization is zero iff $1=0$ in that ring iff there is some $a \in A \setminus \{0\}$ with $a \cdot 1 = 0$ in $B$ iff $A \to B$ is not injective. Thus, the generic fiber of $\mathrm{Spec}(B) \to \mathrm{Spec}(A)$ is integral iff this morphism is dominant. The same holds for general integral schemes.