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State whether the integral converges or diverges and if it converges state the value it converges to.

Integral from 0 to 2 of 1/(1-x)dx

I broke it up into 2 integrals (0 to 1) and (1 to 2) set up the limit for both using variables instead of 1 and I evaluated the integral to equal 0 so I figured it converges to 0 but in my book it says it diverges...it also says it diverges on wolfram alpha so I'm sure that the book is correct, therefore I must be missing something.

Additionally, I took a look at the integral from -1 to 1 of 1/x (which seems very similar to the first problem I stated), yet wolfram alpha says this one is 0.

Why does the second converge to 0 and the first one diverge?

I just learned about improper integrals today so I figure it is likely I am unaware of some detail of problems like these so I would like some help. Thanks.