Number of substrings in a string: n-squared or exponential

Question

How many subtrings are there in a string in general?

Why does string x [1:n] have O(n^2) subtrings according to the lecture 21 Dynamic Programming III of        
6.006 from MIT? 
Why it is not O(2^n)?

Here is a link [http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/MIT6_006F11_lec21.pdf]

Answer 1

Simply a substring is defined by two parameters [i,j] which are start index and end index for substring in the original string . Now 0<=i,j<=n as indices should be within the string, Total values i&j each can have are n so all combinations of [i,j] would be n*(n+1)/2 which is O(n^2)