We study the integrability of Poisson and Dirac structures that arise from quotient
constructions. As our main general result, we characterize the integrability of Poisson
structures which are obtained as quotients of Dirac structures. We illustrate our
constructions by deducing several classical results as well as new applications such as
an explicit description of Lie groupoids integrating two interesting families of
geometric structures:
a special class of Poisson homogeneous spaces of symplectic groupoids
integrating Poisson groups and
