You are ignoring the overlapse. For example the ex.1 Has 1-5 and 1-5. if you were to write every number between the both of them you would indeed get 9 numbers(length 8), but all of them would be dublicated. So the number of the unique numbers is 5(and the length is 4): 1, 2, 3, 4, 5; it is simpler to understand if you write the intervals on one line in a pice of paper. :)

We can forget about 1-5 and 16-19 because they are inside 1-6 an 10-20. 1-6 and 5-11 = 1-11. And 1-11 and 10-20 = 1-20. It's length = 20-1 = 19;