clear all; close all;

N=100;

for jloop=1:3

if jloop==1
    x=linspace(1,5,N);
    dx=x(2)-x(1);
    f1=1./(1+x.^2);
elseif jloop==2
    x=linspace(3,5,N);
    dx=x(2)-x(1);
    f1=x.*sin(x).^2;
else 
    x=linspace(0,10,N);
    dx=x(2)-x(1);
    f1=(x+1).*cos(x);
end    
    
    
F1(1)=0; total1=0;
for j=1:N-1

    F1(j+1)=F1(j)+dx*(f1(j)+f1(j+1))/2;  % cummulative integral
    total1=total1+dx*(f1(j)+f1(j+1))/2;
    
end

% average

ave1=0;
for j=1:N

    ave1=ave1+F1(j);

end
average1=ave1/N

Total(jloop)=total1;

plot(x,f1,x,F1)
hold on

end

Total