A Conflagration of Randomness

Months ago when I started Mechanics in college, my friend and I were discussing kinematics obvioussly and a thought poppped into my head.  What is the intergral of position?  I thought about it all day.  Obviously the units had to be meter*seconds, but what was the meaning?  So I turned to google and discovered that at least one other mind has pondered this question, but as with me, the comprehension just doesn’t make sense.  Read the article here. What do you think?