bugs - Apparently contradictory output from Series and D

I defined a function as:

g[b_] := Integrate[f[n]Exp[-b  DA (n.u)^2], n]

Obviously

 D[g[b], b] /. b -> 0

gives

(-DA)*Integrate[(n.u)^2*f[n], n]

But, then, how can

Series[g[b], {b, 0, 2}]

be

Integrate[f[n], n]

I guess there is something basic I don't understand. Something with order of evaluation? It's like b = 0 is evaluated before the differentiation in Series.