(*^

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:[font = special1; inactive; preserveAspect; ]
                                  Estimation and Limits -- Area -- Reference

The following cell illustrates how Mathematica  can be used to do the calculations involved in this section.  Evaluate it now.
;[s]
5:0,1;76,0;113,2;124,0;188,3;205,-1;
4:2,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,0,0,0;1,13,9,Times,2,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
Clear[Fcn, a, b, n, x]

n := 10

a := 0
b := Pi

Fcn[x_] := Sin[x] + 3

h := (b - a)/n
x[i_] := a + i h

N[Sum[Fcn[x[i]] * h, {i, 1, n}]]  
^*)