Hello, twittytwitter!
A strange problem . . . I think I've solved it.
. . But my approach isn't very formal either.
Suppose that: .
(a) Find: .
The graph of looks like this, for Code:


*    *1
:  R
 +    +    +  
R  :
1o    *


Since the integral represents area,
. . is the total area of the shaded regions below. Code:


*    *1
:::A::: R
 +    +    +  
R :::B:::
1o    *


Since the area of is the negative of the area of ,
. . the total area is 0 (zero).
That is: .
Therefore: .
(b) Repeat (a), but: . . with The graph is a variation of the one in part (a). Code:


*    *1
:::A::: R R+n
 +    +    +   *  
R :::B:::::C::
1o    *   *


Once again, the area of is the negative of the area of
. . And the area of is: .
Hence: .
Therefore: .
c) Does: . . converge or diverge?
As shown in part (a), it converges to 0.