[pgxy2000]

function result=tintergrate()
clear re_n re_2n;
n=1;
eps=0.00001;
x=linspace(0,1,n+1);
h=1/n;
y=x./(4+x.^2);
re_n=(y(1)+y(n+1))*h/2;
for i=2:n
re_n=re_n+y(i)*h;
end
xx=x(1:n)+h/2;
y=x./(4+x.^2);
re_2n=re_n/2;
for i=1:n
re_2n=re_2n+y(i)*h/2;
end
h=h/2;
n=1/h;
x=linspace(0,1,n+1);
while abs(re_2n-re_n)>eps
re_n=re_2n;
xx=x(1:n)+h;
y=x./(4+x.^2);
re_2n=re_n/2;
for i=1:n
re_2n=re_2n+y(i)*h/2;
end
h=h/2;
n=1/h+1;
x=linspace(0,1,n+1);
end
result=re_2n;
%the end