How does this second integral equal +infinity instead of -infinity?

[Lo.Lee.Ta.]

1. ...How does this 2nd integral diverge to +∞? It seems to me that it would diverge to -∞... :/

lim (\frac{-1}{a - 1} - \frac{-1}{0 - 1}) + lim (\frac{-1}{2 - 1} - \frac{-1}{b - 1}) + lim (\frac{-1}{c - 1} - \frac{-1}{2 - 1})
a→1- b→1+ c→∞

2. First integral: -1/(tiny negative #) - 1 = +∞

Second integral: -1 + 1/(tiny negative #) = -1 + -∞ = -∞ <----This answer is supposed to be +∞. How?!

Third Integral: -1/(∞ - 1) + 1 = 0 + 1 = 0

The only thing I don't get it the second integral! :(
Help please!
Thanks! :)

 

[HallsofIvy]

1. ...How does this 2nd integral diverge to +∞? It seems to me that it would diverge to -∞... :/

lim (\frac{-1}{a - 1} - \frac{-1}{0 - 1} + lim (\frac{-1}{2 - 1} - \frac{-1}{b-1}
a→1- b→1+
+ lim (\frac{-1}{c - 1} - \frac{-1}{2 - 1}
c→∞


2. First integral: -1/(tiny negative #) - 1 = +∞

Second integral: -1 + 1/(tiny negative #) = -1 + -∞ = -∞ <----This answer is supposed to be +∞. How?!

It is NOT "tiny negative". -\frac{-1}{b- 1}= \frac{1}{b- 1} and b is approaching 1 from above so b> 1 and b- 1> 0.

Third Integral: -1/(∞ - 1) + 1 = 0 + 1 = 0

The only thing I don't get it the second integral! :(
Help please!
Thanks! :)

 

[Lo.Lee.Ta.]

If b is approaching 1 from the right, it seems like it would be very close to the number 1.

Maybe it would be 1.00000000001

So 1/(1.00000000001 + 1) = 1/.00000000001 = +∞

I usually pay no attention to the - or + in the limit, but I see it's important! O_O
Thanks!

 

[SteamKing]

These are not integrals: they are limits.