I am trying to understand the equation (122)

in http://xxx.lanl.gov/pdf/hep-th/0509097.pdf
Making my proper computation I am obtaining
−∫M4da∧dω12=−∫M4[d2a∧ω12−d(da∧ω12)]=
−∫M4d2a∧ω12+∫M4d(da∧ω12)=
−∫M4d2a∧ω12+∫∂M4da∧ω12=−∫M4d2a∧ω12+0=−∫M4d2a∧ω12
My question is: if my computation is correct and then a minus sign is missing in the last integral of (122)?