yes this is probably a really stupid question, but 1/x doesn't have an integral right?

I wrote a scripting language to graph the areas under the curve (using a numerical approximation algorithm) and on any interval with -x and x (the absolute value of x is the same) I always get an area under the curve of zero, which is what it *seems* like it should be if you consider negative area (then they just cancel), but I can't exactly prove it.

Also, I'm not in college, so if you DO have some fancy proof I probably wont' understand it anyway because i suck

EDIT:

the only thing I can think of is to say that the functions are changing at the same rate when they are the same distance from zero, and that might satisfy that they are approaching the 'same infinity' (i.e i guess you cannot prove that the tangent of x from 0 to PI is approaching the 'same infinity' at pi/2, my math teacher said that one could 'approach infinity before the other' in which case the area is either positive or negative infinity but not zero).