Why is there a differential in an indefinite integral?

I understand why a definite integral of the form [itex]^{b}_{a}[/itex]∫ƒ(x)dx has the differential dx in it. What I don't understand, and what my teacher hasn't explained is why an indefinite integral (i.e. an antiderivative) requires the differential. Why does ∫ƒ(x)dx require that dx to mean "anti-differentiate"? To put it another way, why is the notation for the antiderivative an integral? It's obviously more than a question of notation, however, as without the differential techniques like u-substitution don't work. I hope this question makes sense, but this is something that has been bothering me for a while now. I figured my teacher would get to it eventually, but he hasn't yet.