True-False Determine whether the statement is true or false. Explain your answer. [In each exercise, assume that $f$

and $g$ are distinct continuous functions on $[a, b]$ and that $A$ de-

notes the area of the region bounded by the graphs of $y=f(x),$

$y=g(x), x=a, \text { and } x=b .]$

$$

\text { If } \quad \int_{a}^{b}[f(x)-g(x)] d x=0

$$

$$

\begin{array}{l}{\text { then the graphs of } y=f(x) \text { and } y=g(x) \text { cross at least }} \\ {\text { once on }[a, b] .}\end{array}

$$