  In the first part of this paper, we calculate the disk-level S-matrix
elements of one RR, one NSNS and one NS vertex operators, and show that they
are consistent with the amplitudes that have been recently found by applying
various Ward identities. We show that the massless poles of the amplitude at
low energy are fully consistent with the known D-brane couplings at order
$\alpha'^2$ which involve one RR or NSNS and two NS fields. Subtracting the
massless poles, we then find the contact terms of one RR, one NSNS and one NS
fields at order $\alpha'^2$. Some of these terms are reproduced by the Taylor
expansion and the pull-back of two closed string couplings, some other
couplings are reproduced by linear graviton in the second fundamental form and
by the B-field in the gauge field extension $F\rightarrow F+B$, in one closed
and two open string couplings.
  In the second part, we write all independent covariant contractions of one
RR, one NSNS and one NS fields with unknown coefficients. We then constrain the
couplings to be consistent with the linear T-duality and with the above contact
terms. Interestingly, we have found that up to total derivative terms and
Bianchi identities, these constraints uniquely fix all the unknown
coefficients.
