Интеграл методом прямоугольников

Function ArcSin(X:Real):Real;
BEGIN
    IF ROUND(X*10000000)=10000000 THEN ArcSin:=Pi/2 ELSE
    IF ROUND(X*10000000)=-10000000 THEN ArcSin:=-Pi/2 ELSE
    ArcSin:=ArcTan(X/SQRT(1-X*X));
END;

Function F(x:Real):Real;
begin
 F:=1.0/(x*SQRT(SQR(x)*2-x*3-5.0));
end;

Function Antiderivative(x:Real):Real;
begin
 Antiderivative:=1.0/SQRT(5.0)*arcsin((-x*3-10)/(x*7));
end;

Procedure Rectangle;
var
 i,N:Integer;
 Sum1,Sum2,h:Real;
begin
 N:=5;
 h:=3.0/N;
 Sum1:=0;
 for i:=0 to N-1 do
  Sum1:=Sum1+h*F(3.0+h*i);
 Sum2:=Sum1;
 Repeat
  Sum1:=Sum2;
  N:=N*2;
  h:=3.0/N;
  Sum2:=0;
  for i:=0 to N-1 do
   Sum2:=Sum2+h*F(3.0+h*i);
 Until ABS(Sum2-Sum1)<0.001;
 WriteLn('Rectangle:     ', Sum2:10:5);
end;

Procedure Trapezium;
var
 i,N:Integer;
 Sum1,Sum2,h:Real;
begin
 N:=5;
 h:=3.0/N;
 Sum1:=(F(3.0)+F(6.0))/2*h;
 for i:=1 to N-1 do
  Sum1:=Sum1+h*F(3.0+h*i);
 Sum2:=Sum1;
 Repeat
  Sum1:=Sum2;
  N:=N*2;
  h:=3.0/N;
  Sum2:=(F(3.0)+F(6.0))/2*h;
  for i:=1 to N-1 do
   Sum2:=Sum2+h*F(3.0+h*i);
 Until ABS(Sum2-Sum1)<0.001;
 WriteLn('Trapezium:     ', Sum2:10:5);
end;

Procedure Simpson;
var
 i,N:Integer;
 Sum1,Sum2,h:Real;
begin
 N:=2;
 h:=3.0/(2*N);
 Sum1:=(F(3.0)+F(6.0))/3*h;
 for i:=1 to N do
  Sum1:=Sum1+4.0*h/3.0*F(3.0+h*(2*i-1));
 for i:=2 to N do
  Sum1:=Sum1+2.0*h/3.0*F(3.0+h*(2*i-2));
 Sum2:=Sum1;
 Repeat
  Sum1:=Sum2;
  N:=N*2;
  h:=3.0/(2*N);
  Sum2:=(F(3.0)+F(6.0))/3*h;
  for i:=1 to N do
   Sum2:=Sum2+4.0*h/3.0*F(3.0+h*(2*i-1));
  for i:=2 to N do
   Sum2:=Sum2+2.0*h/3.0*F(3.0+h*(2*i-2));
 Until ABS(Sum2-Sum1)<0.001;
 WriteLn('Simpson:       ', Sum2:10:5);
end;

BEGIN
 Rectangle;
 Trapezium;
 Simpson;
 WriteLn('Accurate value:', (Antiderivative(6.0)-Antiderivative(3.0)):10:5);
 ReadLn;
END.