Let

f:[a,b]->R

be a bounded function on a closed interval

a,b

, let

P={x_(0),x_(1),dots,x_(n)}

be a partition of

a,b

, and let

d

be a real number such that

f(x)

for all

xin[a,b]

.\ (a). Given any

iin{1,2,dots,n}

, show that

l_(i)

, with the

2. Let f:[a,b]R be a bounded function on a closed interval [a,b], let P={x0,x1,,xn} be a partition of [a,b], and let d be a real number such that f(x)d for all x[a,b]. (a). Given any i{1,2,,n}, show that i