The Velocity of a Particle Moving in a Straight Line $v = t \left( t ^ { 2 } + 4 \right) ^ { 4 } + 5 t$

The velocity of a particle moving in a straight line is given by $v = t \left( t ^ { 2 } + 4 \right) ^ { 4 } + 5 t$ .
Given that the distance $s = 0$ at $t = 0$ , find an expression for s in terms of t without any unknown constants.

A) $s ( t ) = \frac { \left( t ^ { 2 } + 4 \right) ^ { 5 } } { 10 } + \frac { 5 t ^ { 2 } } { 2 } - 102.4$
B) $s ( t ) = \frac { \left( t ^ { 2 } + 4 \right) ^ { 5 } } { 10 } + \frac { 5 t ^ { 2 } } { 2 }$
C) $s ( t ) = \frac { \left( t ^ { 2 } + 4 \right) ^ { 5 } } { 2 } + \frac { 5 t ^ { 2 } } { 2 } - 102.4$
D) $s ( t ) = \frac { \left( t ^ { 2 } + 4 \right) ^ { 5 } } { 10 } + \frac { 5 t ^ { 2 } } { 2 } + 102.4$
E) $s ( t ) = \frac { \left( t ^ { 2 } + 4 \right) ^ { 5 } } { 2 } + \frac { 5 t ^ { 2 } } { 2 } + 102.4$