Midpoint rule integration Fourier transform

Hello,

I created the code for Midpoint rule Integration. I am doing the Fourier transfrom. With the code I can get results and plot just for only one '' t''

value. Struggling with making loop and plot for case t = 0:1:2 . There should be 3 lines in the plot.

If somone could help and give a hint?

Thanks

function[]= midpt()
clc;
xl=-pi; % Lowe limit -L
xu=pi; % Upper limit L
N=2; % INtervals beetween -L and L
D=1;

dx = (xu-xl)/N; % dividing the domain into N subintervals
x = xl:dx:xu;
t = 0:1:2 ;  % time

a = xl; 

 for g = 1:length(t) 
    
    f = (@(w) (pi^0.5) * exp((-w^2)/4) * exp (1i*w*x-D*t(g)*w^2)); % FCN
  end 

for k = 1:N+1
    b = a+dx;
   
    M(k,:) = (b-a)* f((a+b)/2); % Midpoint rule
    a=b;
    
    I= sum(M); % Integral
    
    end


plot(x, I, 'Linewidth', 2)
xlabel('x')
ylabel('c(x,t)')


axis tight
    



 
end