  We consider embedded, smooth curves in the plane which are either closed or
asymptotic to two lines. We study their behaviour under curve shortening flow
with a global forcing term. Firstly, we prove an analogue to Huisken's distance
comparison principle for curve shortening flow for initial curves whose local
total curvature does not lie below $-\pi$, and show that this condition is
sharp. Secondly, for bounded forcing terms, we exclude singularities in finite
time. Thirdly, for immortal flows of closed curves whose forcing terms provide
non-vanishing enclosed area and bounded length, we show convexity in finite
time and smooth and exponential convergence to a circle.
