Mr. Gauss is known for his indecisiveness! He will often walk down the hallway toward his office, change his mind, turn around, and then turn around again! One time he left class when the bell rang ($t = 0$) traveling with velocity in feet per second given by $v(t) = 3t^2 - 17t + 10$. After $7$ seconds, he arrived at his office.

1. Calculate the total distance he traveled during the $7$ seconds.

   Hint (a):

   $=\text{total distance }=\int_{t=a}^{t=b}\text{ speed }dt=\int_{t=a}^{t=b}\left | \text{velocity} \right |dt$

2. Assuming he traveled back and forth in a straight line, how far is his classroom from his office?

   Hint (b):

   $\text{displacement }=\int_{t=a}^{t=b}\text{velocity } dt$