It is trivial to show that the bottle, burger and handles (to use a little-known antipodean measure) unknowns are 10, 5 and 2 respectively, so our limits are 0 and infinity. I'm sure at one stage I knew how to prove the definite integral of sin(x)/x between 0 and infinity is pi/2. Just like my undergrad days, my first port of call was The Integrator, now integrated into the Wolfram Alpha borg. But that doesn't really help in this case, as the indefinite integral is just a big ugly series... so let's look elsewhere, oh something to do with Laplace transforms, now I'm getting nostaligic. We'll leave this as an exercise for the reader.

Anyhoo with wikipedia kindly solving the hard bit for us all we need to do is multiply pi/2 by bottle/handles = 10 / 2, so simplifiying gives 5 * pi / 2 . Maybe?

Yay i used my terminal degree