kinematics, integrate constant a

• With initial condition $v(t_0) = v_0$, velocity becomes $$\tag{G1} v(t) = v_0 + a(t - t_0). $$
• With initial condition $x(t_0) = x_0$, position becomes $$\tag{G2} x(t) = x_0 + v_0 (t - t_0) + \tfrac12 a (t - t_0)^2. $$
• Are they the same as the first two of common kinematic equations?