The particle impulse momentum relationship was derived already for particles here and planar rigid body here. In 3d it is also true that the sum of forces acting on the body is related to the time rate of change of the linear momentum:
\sum \mathbf F = \frac{\mathrm d \mathbf P}{\mathrm d t}
Similarly, the angular impulse and the change in angular momentum:
\int_{t_1}^{t_2} \sum \mathbf M_C \, \mathrm d t = \Delta \mathbf L_C = \mathbf L_{C_f} - \mathbf L_{C_i}
For linear motion, integrating the forces gives the linear impulse and change in linear momentum:
\int_{t_1}^{t_2} \sum \mathbf F \, \mathrm d t = \Delta \mathbf P = m \mathbf v_{C_f} - m \mathbf v_{C_i}
For angular momentum is it necessary to write the angular momentum in 3D. Considering the center of mass it takes the form:
\mathbf L_C = \mathbf I_C \boldsymbol \omega = \begin{bmatrix} I_{xx} & I_{xy} & I_{xz} \\ I_{xy} & I_{yy} & I_{yz} \\ I_{xz} & I_{yz} & I_{zz} \end{bmatrix} \begin{bmatrix} \omega_x \\ \omega_y \\ \omega_z \end{bmatrix}