A note on the role of the boundary terms for the non-Gaussianity in general k-inflation

In this short note we clarify the role of the boundary terms in the calculation of the leading order tree-level bispectrum in a fairly general minimally coupled single field inflationary model, where the inflaton's Lagrangian is a general function of the scalar field and its first derivatives. This includes k-inflation. DBI-inflation and standard kinetic term inflation as particular cases. These boundary terms appear when simplifying the third order action by using integrations by parts. We perform the calculation in the comoving gauge obtaining explicitly all total time derivative interactions and show that a priori they cannot be neglected. The final result for the bispectrum is equal to the result present in the literature which was obtained using the field redefinition.