Questions about Section 1.2 on page 11

[Min Zhang]

I have been reading the textbook and found the following part that I don't quite understand:

At the top of page 11, it says

By the chain rule the left side of Eq. (6) is the derivative of ln|p-900| with respect to t, so we have  $d/dt\ ln|p-900| = 1/2$.

Then, by integrating both sides of Eq. (7), we obtain  $\ln|p-900| = t/2+C$

So my questions are:

1. Why can we get those statements?

2. Why do we have to insert a constant number $C$?

Thank you very much!

[Victor Ivrii]

In virtue of elementary knowledge of Calculus I.