A cart moves along a straight horizontal track, and a sensor records its instantaneous velocity v at equal time intervals of \(\Delta t = 2.0\text{ s}\), as shown in the table.

Time \(t\text{ (s)}\)	\(0.0\)	\(2.0\)	\(4.0\)	\(6.0\)
Velocity \(v(t)\text{ (m/s)}\)	\(3.0\)	\(7.0\)	\(13.0\)	\(21.0\)

The velocity of the cart is strictly increasing with non-constant acceleration over the entire time interval from \(t = 0.0\text{ s}\) to \(t = 6.0\text{ s}\). Which of the following correctly identifies the left-endpoint Riemann sum approximation \(\Delta x_L\), the right-endpoint Riemann sum approximation \(\Delta x_R\), and the relationship of the true displacement \(\Delta x = \int_0^6 v(t)\,dt\) to these approximations?