Question

Give an example of a function that is integrable on the interval [-1,1], but not continuous on [-1,1]. explain.

Answer 1

With an absolute value somewhere in the formula, you can create a discontinuous function.

how about f(x) = |x|/x

It jumps from -1 to +1 at x=0, yet it can be integrated on [-1,1]. The surface is 2.