Signed area and total area

You will write functions that find the signed area and the total area of a curve with thin strips, and a test for a curve whose signed area cancels to zero. The checker uses a parabola, a sine wave and a cubic.

The idea. A strip below the axis has a negative height $f(x)$. Adding the heights with their signs gives the signed area. Adding the absolute values $\lvert f(x) \rvert$ gives the total area. A curve can have signed area $0$ and still enclose a region.

Your tasks.

1. Finish signed_area(f, a, b, n). Add f(middle) * width for each of the n strips.
2. Finish total_area(f, a, b, n). Do the same with the absolute value of the height.
3. Finish cancels(f, a, b). Return True when the signed area is within 0.001 of zero and the total area is larger than 0.001.