Mathematics

Problem

An increasing function

h

[2,6]

satisfies

L_{50}=8.2

and

R_{50}=9.1

, where the sums use 50 equal subintervals. Provide the sharpest bound you can for

\displaystyle \int_{2}^{6} h(x)\,dx

and state the maximum possible error if either

L_{50}

R_{50}

is used as the estimate.