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Integrating signed velocity $v(t)$ accumulates forward motion positively and backward motion negatively, resulting in net displacement ($\Delta x$). Integrating absolute velocity $|v(t)|$ treats all motion as positive contribution, regardless of direction, thereby summing up the total ground covered (total distance).

Conditions: Motion occurs along a 1D line; Velocity $v(t)$ changes sign

Integrating signed velocity $v(t)$ accumulates forward motion positively and backward motion negatively, resulting in net displacement ($\Delta x$). Integrating absolute velocity $|v(t)|$ treats all motion as positive contribution, regardless of direction, thereby summing up the total ground covered (total distance).

Conditions: Motion occurs along a 1D line; Velocity $v(t)$ changes sign