Find lower and upper estimates of the integral

[violet]

Hi, my question is:

Consider the integral of 1/(t(t+1)) with respect to t, from lower limit t=0 to the upper limit t=n, where n is an arbitrary positive integer.
Let P be the partition {1, 2, ..., n}. Find lower and upper estimates L(P) and U(P) for the integral above. Simplify your answer as far as possible.

I know that you need to use Riemann's integral for this question, so here is my working so far:

L(P)= sum from i=1 to n of g(t(i-1))(t(i)-t(i-1))
t(i)-t(i-1)=(n-1)/n
g(t(i-1))=1/(t(i-1))(t(i-1)+1)
Then if I put these back into the equation for L(P), I should get the lower estimate. However, I end up getting a complicated summation, and I'm not sure about how to simplify it, or if it's even correct. Here is the summation that I get when finding L(P):

sum from 1 to n of (n(n-1))/(t(i-1)(t(i-1)+1))

Where t(i-1)=1+i(n-1)/n

[Note: the (i-1) part is subscript, but I wasn't sure how to show it.]

Could you tell me if I'm on the right lines here, or if I'm completely incorrect? And if it's completely wrong, could you please help me? Thank you!

 

[Bob Brown MSEE]

Are you sure the integral is 0 to n? Not 1 to n?

The upper bound of the first partition " from lower limit t=0 to the upper limit t=1 " , is infinite.
So all upper bounds are infinite, and not very useful.