Chapter 5.1, Problem 19E

(a)

To determine

To sketch: The graph of $f\left(x\right)=x+1$ on the interval $\left[1,4\right]$.

(b)

To determine

To calculate: The value of $\Delta x$ and the grid points.

(c)

To determine

To illustrate: The left Riemann sum and the right Riemann sum of the function.

$f\left(x\right)=x+1$ on the interval $\left[0,4\right]$ for $n=4$; determine which Riemann sum underestimates and overestimates the area under the curve.

(d)

To determine

To find:  The left and right Riemann sums of $f\left(x\right)=x+1$ on the interval $\left[1,4\right]$.