Problem $3$ Suppose the graph of the velocity function $v$ looks like this:

$($a$)$ How far does the car travel between time $t=1$ hours and $t=1+dt$ hours? What does your answer describe, geometrically, in the graph. Explain your reasoning.

$($b$)$ Describe, in terms of the geometry of the graph, how far the car travels between time $t=1$ hours and time $t=3$ hours? Explain your reasoning.