Stoermer's Rule:

 X = 0.0000 to 1.5708 in  5 steps
    Integration    Answer
     2.583344    2.570796
     0.460868    0.467400
 X = 0.0000 to 1.5708 in 15 steps
    Integration    Answer
     2.572169    2.570796
     0.466682    0.467400
 X = 0.0000 to 1.5708 in 25 steps
    Integration    Answer
     2.571290    2.570796
     0.467142    0.467400
 X = 0.0000 to 1.5708 in 35 steps
    Integration    Answer
     2.571048    2.570796
     0.467269    0.467400
 X = 0.0000 to 1.5708 in 45 steps
    Integration    Answer
     2.570949    2.570796
     0.467320    0.467400