Clarification on Definite Integrals

Hello, and thanks in advance for your help.

The problem I'm facing is to integrate by parts the following function:

lnx/x^2 with the interval of integration being from 1 to 2.

I don't think I need a full solution, it's just that after I do the integration by parts method, I'm left with no integrals, and this makes me concerned. Is the answer to this problem simply my simplified 1/3x^3lnx - 1/9x^3 or is it this simplification with the values 2 inputted for x subtracted from it with 1 inputted for x (like shown below)?

[1/3*2^3*ln2 - 1/9*2^3] - [1/3*1^3*ln1 - 1/9*1^3]

Thanks again for the assistance...I think it's just a matter of not understanding how the interval of integration given at the start of the problem relates to my solution.

Correction and Restatement of Question