The graphs in Figure 4.2.6(a) are controlled by the slider beneath them. Each graph is drawn from $x\=-2$ to the value set by the slider.

For slider values to the left of $x\=-2$, the graph of $f$ on the left is drawn "backwards" since the trace is leftward from $x\=-2$. The area between the graph of $f$ and the $x$-axis is shaded in yellow.

The function $F\left(x\right)$ is drawn on the right in Figure 4.2.6(a). For slider values to the left of $x\=-2$, the definite integral determining $F$ has its upper limit to the left of the lower limit, which negates the value of the integral. Since the area for these values of $x$ is negative, the value of $F$ is positive.

By Property (1) of Table 4.2.1, $F\left(-2\right)\=0$ (the upper and lower limits are the same).

For slider values to the right of $x\=-2$, the graph of $f$ on the left shows only area to the right of $x\=-2$, and the graph of $F$ on the right shows only the value of the definite integral from $-2$ to $x\>-2$. The function $F$ is decreasing where $f$ is negative, and increasing where $f$ is positive.