Solve the Problem $\mathrm { v }$ (In $\mathrm { ft } / \mathrm { s }$

Solve the problem.
-During each cycle, the velocity $\mathrm { v }$ (in $\mathrm { ft } / \mathrm { s }$ ) of a robotic welding device is given by $\mathrm { v } = 2 \mathrm { t } - \frac { 10 } { 36 + \mathrm { t } ^ { 2 } }$ , where $t$ is the time (in s) . Find the expression for the displacement $s$ (in $\mathrm { ft }$ ) as a function of $t$ if $s = 0$ for $t = 0$ .

A) $s = t ^ { 2 } - \frac { 5 } { 3 } \tan ^ { - 1 } \left( \frac { t } { 6 } \right)$
B) $s = t ^ { 2 } - 10 \sin ^ { - 1 } \left( \frac { t } { 6 } \right)$
C) $s = t ^ { 2 } - 10 \tan ^ { - 1 } \left( \frac { t } { 6 } \right)$
D) $s = t ^ { 2 } - \frac { 5 } { 3 } \tan ^ { - 1 } \left( \frac { 5 } { 3 } t \right)$