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

$$-\int_{M^4}da \wedge d\omega_{2} ^{1}=-\int_{M^4}[d^2a \wedge\omega_{2} ^{1}-d(da \wedge \omega_{2} ^{1}) ]=$$

$$-\int_{M^4}d^2a \wedge\omega_{2} ^{1}+\int_{M^4}d(da \wedge \omega_{2} ^{1}) =$$

$$-\int_{M^4}d^2a \wedge\omega_{2} ^{1}+\int_{\partial M^4}da \wedge \omega_{2} ^{1}= -\int_{M^4}d^2a \wedge\omega_{2} ^{1}+0= -\int_{M^4}d^2a \wedge\omega_{2} ^{1}$$

My question is: if my computation is correct and then a minus sign is missing in the last integral of (122)?