Why can the definite integral of a function f from a to b be interpreted as the net sign area...?

30 Views Asked by At

between the graph of f and the interval [a,b], only if f is continuous?

This is what my textbook mean by "net sign area": enter image description here

I don't think f has to continuous for this to be true. For example, f can be like this: enter image description here ...and there to me is still a net sign area.