One easy example on the field of physics are those problems related to finding the electrical / graviational /etc. potential of a given field. For example, the electric potential created by a charged sphere of radius $R$ for  $r \geq R$ is given by:

$$  V(r) = - \int_{\infty}^r E(r) \, \mathrm{d}r$$ where $E$ is the electric field (modulus) generated by the sphere and $r$ is the distance from the center of the sphere. This also has a very simple physical meaning since the integral (when the minus sign is considered) represents the work to be done by somebody (or something) to bring the considered amount of electrical charge (responsible for creating the electric field $E$) from $\infty$ to $r$. 

The same expression and physical meaning can be applied to the case of gravitational potential.

Cheers!

Practical use and applications of improper integrals
As a follow up to this etymology question, does "so far, so good" carry a negative connotation?

For example, after having her sonogram, my wife asked the technician if everything was okay.  The technician replied, "so far, so good."  My wife later remarked that she didn't like that the technician used the phrase because it sounded like things will be going wrong later.

I always thought this phrase was positive and that it was a replacement for the word "good."
