  Using tools from Dirac geometry and through an explicit construction, we show
that every Poisson homogeneous space of any Poisson Lie group admits an
integration to a symplectic groupoid. Our theorem follows from a more general
result which relates, for a principal bundle $M\to M/H$, integrations of a
Dirac structure on $M/H$ to $H$-admissible integrations of its pullback Dirac
structure on $M$ by pre-symplectic groupoids. Our construction gives a
distinguished class of explicit real or holomorphic pre-symplectic and
symplectic groupoids over semi-simple Lie groups and some of their homogeneous
spaces, including their symmetric spaces, conjugacy classes, and flag
varieties. In a more general framework, we also show integrability of all
homogeneous spaces of ${\mathcal{LA}}^\vee$-Lie groups in the sense of E.
Meinrenken.
