$(5$ points$)$ The velocity $v(t)$ in the table below is increasing for $0t12.$

A$.$ Find an upper estimate for the total distance traveled using

$n=4$ subdivisions: distance traveled $=$

$n=2$ subdivisions: distance traveled $=$

B$.$ Which of the two answers in part $($A$)$ is more accurate?

$n=$

is more accurate

$($Be sure that you can explain why!$)$

C$.$ Find a lower estimate for the total distance traveled using $n=4.$

distance traveled $=$