​ Examine the equation $x ( 1 ) + \int _ { 1 } ^ { 7 } v ( t ) d t = 22$ where $v$ represents the velocity of a particle moving along the $x$-axis on a sheet of centimeter grid paper in cm/sec. At $t=1$, the particle is at the point $(7,0)$.

1. Write a complete description about what the integral $\int _ { 1 } ^ { 7 } v ( t ) d t$ is computing. Use correct units and be sure to mention the meaning of the bounds in your description.

   Hint (a):

   What does the integral of velocity represent?

2. In the context of the problem, what does the value $22$ represent?

   Hint (b):

   $x\left(1\right)$ represents the position of the particle at $t=1$. Add this to the integral which you described in part (a), and the sum is $22$.

3. Evaluate $\int _ { 1 } ^ { 7 } v ( t ) d t$.

   Hint (c):

   According to the last sentence of the problem, $x(1)=7$.