Hey Kiwi_Dave.

You could show that the function f is Integrable over some region (Riemannian Integrable) and that would suffice. Showing Riemannian Integrability can be shown if you have two functions that are Riemann Integrable then the product is Riemann Integrable (I've seen this proof on a pdf somewhere so you can search for it if you want).

I suggest this way to split up the Langrangian with bt/m and the other term.

Once you do this, you will have shown that an anti-derivative exists, and you're done.