Has anyone read Atiyah and Bott's famous paper "The moment map and equivariant cohomology"?

I have some trouble with the equaations appearing between equations (4.18) and (4.19) in page 13 of the original paper. The paper claims $$D\lambda a = D(a-i(X)a\theta) = da-i(X)da \theta + i(X)au,$$ whereas I think that it should be $$D\lambda a=D(a-i(X)a\theta)=da+i(X)da\theta + i(X)au,$$ where the minus sign is due to $\mathcal{L}(X)a=i(X)da+di(X)a = 0$.

Can anyone tell me what it should be?

Thank you!