  Moore and Yang defined an integral notion, based on an extension of Riemann
sums, for inclusion monotonic continuous interval functions, where the
integrations limits are real numbers. This integral notion extend the usual
integration of real functions based on Riemann sums. In this paper, we extend
this approach by considering intervals as integration limits instead of real
numbers and we abolish the inclusion monotonicity restriction of the interval
functions and this notion is used to determine interval probability density
functions.
