Finite difference method Boundary conditions

How to set the boundary conditions and initial conditions for the problem mentioned below?. I tried the below mentioned code. But it seems it's not correct.

% Simulation of a 1-D Linear Convection model by a time march (Finite
...Difference Method)
% Numerical scheme used is a first order upwind in both space and time
%%
clc;
clear;
%Specifying Parameters
xr=1; % Space(x) right side limit
xl=0; % Space(x) left side limit
dx=0.05;%Width of space step             
x=xl:dx:xr;%Range of x (0,1) and specifying the grid points
nx=length(x);%Number of steps in space(x)  
tr=20; % time(t) right side limit
tl=0; % time(t) left side limit
dt=0.04;%Width of each time step
t=tl:dt:tr;
nt=length(t);
a=1.0; 

 for i=1:nx
     u(i,1)=(sin(pi*x(i)))^40;%%%Initial conditions
 end
for x=1:nx-1
    for t=1:nt-1
        u(x,t+1)=u(x,t)+(dt/dx)*(u(x+1,t)-u(x,t));
        u(end,t)=u(1,t);%%%Boundary conditions
    end    
end