how would you do this improper integral

Question

1/(x-1)
from 0 to 2

this is improper at one, so I split it up into two integrals
ln(x-1) from 0-1 and
ln(x-1) from 1-2

I then did for the first one the (lim t->1(-) of ln(t-1))-(ln(0-1))

and then the same thing for the second part
I didn't know if this was right though, or what the answer would be

Answer 1

Did you read my previous answer?

Answer 2

yes, but I wasn't sure of the final answer from your answer.

Answer 3

I left the final calculation up to you. If you define the integral as the sum of two parts that each approach within a distance a of x=1, and let a gapproach zero, than the answer will be zero because the two parts will always cancel, not matter how small a is.