$1.[$FTC$4]$ Suppose that a person is walking in such a way that her velocity $\backslash ($ v$($t$)\backslash )$ varies slightly according to the information given in the table.

a$.$ Using the given data, estimate the distance travelled by the walker during the two hour interval from $\backslash ($ t$=0\backslash )$ to $\backslash ($ t$=2\backslash )$ using time intervals of width $\backslash (\backslash$Delta t$=0\mathrm{.}5\backslash )$ and using a right$-$hand$-$sum. Include the units for distance. In the graph below, shade the regions described by the estimated distance.