Evaluate the integral

Work = Integrate[m a[x], {x, a, b}]

by replacing a[x] by v[x] v'[x] to get

Work = Integrate[m v[x] v'[x], {x, a, b}]

and then using the pairings

m v[x] <--------------> m v

v'[x] x <----------> v

Subsuperscript["", a, b]<------------------->Subsuperscript["", v[a], v[b]]

to get a formula for work in terms of the velocities v[a] at x = a and v[b] at x = b.

The formula that you get will show that the work measurement done does not depend on the explicit nature of the force. The force may vary in magnitude in any imaginable way provided that the velocities at the two endpoints, v[a] and v[b], do not change. In other words, the work measurement depends only on the mass and the beginning velocity v[a] and the terminal velocity v[b].