## Examples 7.1.13(c):

If

Since *f*is an integrable function defined on*[a, b]*, which is bounded by*M*on that interval, prove thatM (a - b) f(x) dx M (b - a)

*f*is bounded on

*[a, b]*by

*M*we know that

Therefore:-M f M

or equivalently (we have computed the left and right integrals before):-M dx f(x) dx M dx

-M (b - a) f(x) dx M (b - a)