sum = 0;%the sumn
n = 2;%the number of intervals\
pi = 3.141592654;
a = (10^-10)/pi;%lower limit
b = 1/(2*pi);%upper limit
I = .022560661746;%the real integral value

for n = 2:2*n:256
for x = a:(b-a)./n:b
    f = sin(1./x);%the function
    
    if x == a
        sum = sum + f./2;
    end
    
    if x == b
        sum = sum + f./2;
    end
    
    if x > a && x < b
        sum = sum + f;
    end
end
T = sum.*(b-a)./n;
Error = I - T;
hold on
loglog(abs(Error), (b-a)./n,'.')
end