The Acceleration Function (In M $S^{2}$ ) and the Initial Velocity Are Given for a Particle

The acceleration function (in m/ $S^{2}$ ) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval. $a(t) =t+4, v(0) =5,0 \leq t \leq 10$

A) $v(t) =\frac{t^{2}}{2}+5 t \mathrm{~m} / \mathrm{s}, 566 \frac{2}{3} \mathrm{~m}$
B) $v(t) =\frac{t^{2}}{2}+5 \mathrm{~m} / \mathrm{s}, 616 \frac{2}{3} \mathrm{~m}$
C) $v(t) =\frac{t^{2}}{2}+5 t \mathrm{~m} / \mathrm{s}, 591 \frac{2}{3} \mathrm{~m}$
D) $v(t) =\frac{t^{2}}{2}+4 t+5 \mathrm{~m} / \mathrm{s}, 416 \frac{2}{3} \mathrm{~m}$
E) $v(t) =\frac{t^{2}}{2}+4 t+5 \mathrm{~m} / \mathrm{s}, 516 \frac{2}{3} \mathrm{~m}$