$B(0)+\int_0^{364}B^\prime(t)dt=212$ , where $B$ represents the number of “buddies” you have in your buddyzone.com account $t$ is days since your $16$^th birthday.

1. In the context of the problem, write a complete description about what the integral is computing. Use correct units and be sure to mention the meaning of the bounds in your description.

   Hint (a):

   Recall that integrals can be considered accumulation functions.

2. If $\int _ { 0 } ^ { 364 } B ^ { \prime } ( t ) d t = 115$, how many buddies did you have on your $16$^th birthday? Justify your answer.

   Hint (b):

   $B(0)$ represents the number of buddies you have on your $16$th birthday.