We can also find the displacement of a moving object from its velocity–time graph. This is given by the area under the graph:

displacement = area under velocity–time graph

It is easy to see why this is the case for an object moving at a constant velocity. The displacement is simply velocity $ \times $ time, which is the area of the shaded rectangle (Figure 2.6a).
For changing velocity, again the area under the graph gives displacement (Figure 2.6b).

Figure 2.6: The area under the velocity–time graph is equal to the displacement of the object.

So, for this simple case in which the area is a triangle, we have:

$\begin{array}{l}
displacement = \frac{1}{2} \times base \times height\\
 = \frac{1}{2} \times 5.0 \times 10\\
 = 25m
\end{array}$

It is easy to confuse displacement–time graphs and velocity–time graphs. Check by looking at the quantity marked on the vertical axis.
For more complex graphs, you may have to use other techniques such as counting squares to deduce the area, but this is still equal to the displacement.
(Take care when counting squares: it is easiest when the sides of the squares stand for one unit. Check the axes, as the sides may represent 2 units, 5 units or some other number.)