  We examine the known curvature terms in the DBI part of the D-brane action
under the T-duality transformation. Using the compatibility of the action with
the standard rules of T-duality at the linear order as a guiding principle, we
include the appropriate NS-NS $B$-field terms in the action and show that they
reproduce the O(\alpha'^2) terms of the corresponding disk-level scattering
amplitude.
