For an analytic F with F′ = f, the integral ∫ f dz = F(b) − F(a) depends only on the endpoints. Draw several paths between the same two points in the left plane — their images F(path) all end at the same place on the right. The blue arrows show the direction field of f.
A modern JavaScript + Canvas port of a 2000 Java applet by Terence Tao
(originally FtocApp.java / FtocGrid.java).
Draw a path; F traces it on the right. Its endpoint is F(b) − F(a).