Finite difference method using upwind scheme

Problem:

My code:

% clear workspace
clear
clc

% define variables
xmin = 0;
xmax = 1;
t = 0;
tmax = 1;
h=input("Enter the temporal step size h = ");
dx=input("Enter the spatial step size dx = ");
N = (xmax-xmin)/dx; % No of nodes

%discretize the domain
x = xmin : dx : xmax;

%calculate intial condtions
u0 = x+1;
u = u0;
unp1 = u;

%march fds through time
nsteps = ceil(tmax/h);

for n = 1 : nsteps
    
    %boundary condtions
    u(1) = exp(-t);
    
    % calculate upwind scheme for a>0
    for i = 2: N+1
         unp1(i)= u(i)-(x+1)*h/dx*(u(i)-u(i-1));
    end
    
    % calculate exact solution
    exact = (x+1)*exp(-t);
    % error calculation
    err = abs(unp1-exact);
    % update u
    u = unp1;
    x= x+dx;
    t = t+h;
    
    % plot solution
    plot(x,exact,'r-')
    hold on
    plot(x,u,'o-')
    hold off
    axis ([0 1 0 1])
    shg
    pause(h)
    
end

I'm not sure whether I coded the intial and boundary condtions correctly or not? Please correct me if I am wrong. Also, I'm getting error while run becasue of the term (x+1) inside the for loop. I understand that I need to create a loop for x but have no idea how can I do that since I discretized the domain already. Please help me with that. Thank you!