9.2.1 Riemann Integral

. . Riemann Integral Consider a real-valued, bounded function f x ( ) defined on the closed and bounded interval [ , ], a b The function ( ) need not have the same sign on [ , ] a b ; that is, f x may have positive as well as negative values on [ , ] a b . See Fig . . Partition the interval [ , ] a b into n subintervals [ ],[ , ], ,[ ],[ ] x x x x  such that  In each subinterval [ ], , , , , i i i  choose a real number ξ i arbitrarily such that i i i − ≤ ξ Consider the sum i i i i ( )( ξ