How accurate is the following assertion?
A function is Riemann-integrable (necessarily over an interval) iff.:
(1) it is defined on the interval, except perhaps at the end-points, and
(2) it is bounded on the interval, and
(3) it is continuous on the interval, except at a finite number of points.
EDIT: Revised assertion based on the answers given:
A (bounded) function is Riemann-integrable (over a closed interval) if:
it is continuous on the interval, except at a finite number of points.