I'm not quite sure what the definition of "doesn't exist" is supposed to be because any integral that is (+/-) infinity doesn't exist, so A and C should be the same!

Regardless, look at the form of the integrand for large x (which translates in this case for any x greater than 5 - 10 or so.)

So compute

.

This by itself is not an answer, but if you sketch the integrand over [1, 10] you will see that the area under the curve is clearly finite. Thus

Since this answer isn't listed, it must be answer D.

-Dan