Hello, wjn1982!
Original integration: .$\displaystyle \int^2_1\frac{1}{x}\,dx$
Problem: need limits to be 0 and 1.
How do i change the 1/x when i change the limits?
If I understand the problem, we have a horizontal translation . . .
The original integral represents the area under $\displaystyle y \,=\,\frac{1}{x}\,\text{ from }x = 1\text{ to } x = 2$ Code:
*

 *
 *
 *.
 :::::*
 :::::
   +   +   +  
 1 2
To maintain the same area, using limit $\displaystyle x = 0\text{ to }x = 1$
. . the graph looks like this: Code:
* 

* 
* 
*.
:::::*
:::::
   +   +  
0 1
The graph is moved one unit to the left.
Therefore, the function would be: .$\displaystyle y \:=\:\frac{1}{x+1}$