Question: The graph of \(f\left( x \right)=\frac{x}{{{x}^{2}}+1}\) is shown below for x > 0. Estimate the area under the curve on the interval [0,4] by evaluating:

a) The right-hand sum \(\sum\limits_{i=1}^{4}{f\left( {{x}_{i}} \right)}\Delta x\), for \(\Delta x=1\)

b) The left-hand sum \(\sum\limits_{i=0}^{3}{f\left( {{x}_{i}} \right)}\Delta x\), for \(\Delta x=1\)