when to use ( end point/date - start point/date + 1) , and when to use end point /date - start point /date?

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This is a simple question on difference. I have seen the following situation - for example how many day you spend on a travel when the travel date was 14-Aug-2014 till 25-August-2014. The answer for this is 25-14+1, which is 12 days. However, if I would have just subtracted, then the answer would have been 11, which is wrong. Now, the question, when I should do the difference + 1, and when I should just subtract. What is the idea behind it? How to identify when to apply what? The date part I know is just by experience, but I am worried I might fail in a similar situation where the application is different. Can someone please explain me this in detail?