what does it mathematically mean an integral of a vector ? for example in physics we say that the impulse $\vec{I}$ is the time integral of force $\vec{f}$ : 

$\vec{I} = \int\_{t\_{1}}^{t\_{2}} \vec{f} dt$ 

what does this object $~~ \int\_{t\_{1}}^{t\_{2}} \vec{f} dt$ clearly mean ? is it a vector ? does it have the same direction as $\vec{I}$ ?