first, there should not be two dx, im pretty sure the dx on the left should be 1, not dx
you first write the expression as 1/((x+2)(x-1)), use partial fraction, so the expression becomes A/(x+2)+B/(x-1), solve for A and B and you will get -1/3 and 1/3 respectively. If you don't know how to solve for A and B, please read over http://en.wikipedia.org/wiki/Partial_fraction
the integral of -1/(3*(x+2)) and 1/(3*(x-1)) are -ln(x+2)/3 and ln(x-1)/3. This expression can be written as ln((x+2)/(x-1))/3. Taking the limit, and you will get -ln(4)/3
Sry, my chinese isn't good enough for me to explain something like this in chinese, but hope my explanation makes sense to you.
