Which expression correctly gives the impulse delivered by a time-dependent force $F\left(t\right)$ between times $t_1$ and $t_2$?

$J=F\left(t_2\right)-F\left(t_1\right)$

$J={\int }_{t_1}^{t_2}m\cdot a\left(t\right)\cdot tdt$

$J={\int }_{t_1}^{t_2}t\cdot F\left(t\right)dt$

$J={\int }_{t_1}^{t_2}F\left(t\right)dt$