**velocity**of an object using the

**position-time**graph. We can do the reverse: given the

**velocity-time**graph, we can calculate the change in

**position**.

Recall that \(v = \frac{dr}{dt} \implies r = \int v(t) dt\). So, the displacement of an object is the integral of velocity. Whenever you see an

**integral**, think of

**area under the curve**. If the curve is

**below**the y-axis, the area is

**negative**.

For example, the area in the first rectangle in the animation equals the displacement from \(t=0\) to \(t=1\). The area of the second rectangle equals the displacement from \(t=1\) to \(t=3\).