This applet is a variant of Applet 6, Complex
Integration. The main differences are that (a) all the functions
`f(z)` have a primitive `F(z)`, and (b) an integral from
`z_1` to `z_2` will start from `F(z_1)` (and hence
end up at `F(z_2)`) rather than starting at 0 as in Applet 6 (in
which case the integral would end up at `F(z_2) - F(z_1)`, as per
the fundamental theorem of calculus.

If the mouse is at a location `z`, and you drag the mouse by
small amount `dz`, then the integral moves from `F(z)` to
`F(z + dz)`. Since `F'(z) = f(z)`, the net change in
the integral is roughly
`f(z) dz` - the same as in Applet 6.
As before, The cyan and green lines indicate the direction the integral
would move by if you moved `z` rightward or upward respectively;
they represent the complex numbers `f(z)` and `i f(z)` respectively.

When you integrate `f` on a closed loop, you always get 0 - providing
that the function f has an anti-derivative on all of the loop. In
the applet below, there are some cases (when f(z) = 1/z) when the function
F(z) sometimes fails to be an anti-derivative, in which case the right-hand
screen fails to correctly compute the integral.