MathCS.org - Real Analysis: Examples 7.1.13(c):

Examples 7.1.13(c):

If f is an integrable function defined on [a, b], which is bounded by M on that interval, prove that

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

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Since f is bounded on [a, b] by M we know that

-M f M

Therefore:

-M dx f(x) dx M dx

or equivalently (we have computed the left and right integrals before):

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

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