this is easy, just use partial fraction

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.