  We construct an infinite-dimensional symplectic 2-groupoid as the integration
of an exact Courant algebroid. We show that every integrable Dirac structure
integrates to a "Lagrangian" sub-2-groupoid of this symplectic 2-groupoid. As a
corollary, we recover a result of Bursztyn-Crainic-Weinstein-Zhu that every
integrable Dirac structure integrates to a presymplectic groupoid.
