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The function is;

$f\left(x\right)=5$

Here we are finding example of a graph of a function $f$ on interval $[a,b]$for which the left sum with four rectangles finds the exact area under the graph from $x=atox=b$.

The function is,

$f\left(x\right)=5$

Therefore, the example is${鈭�}_a^{b}5dx.$

The given function is,

$f\left(x\right)=5$

The objective is to find example of a graph of a function $f$on interval $[a,b]$for which all trapezoid sum finds the exact area under the graph from $x=atox=b$.

The function is,

$f\left(x\right)=5$

Therefore, the example is${鈭�}_a^{b}5dx$.

The function is,

$f\left(x\right)=3x+1$

The objective is to find an example in which the upper sum for $4$rectangles is a much better approximation than the lower sum with $4$rectangles.

The function is,

$f\left(x\right)=3x+1$

The interval is,

$[a,b]=[3,5]$

The value of$n$is$4.$