How to make convolution code without using conv

I want to make convolution without using 'conv'. The code in below is that I did, and right side of a attached pic is result that I should make.

clc
clear
close all

t= -5:0.001:5;
x= (t>=0)&(t<=1);
h= (t>-2)&(t<0);

X=[x,zeros(1,length(t))];
H=[h,zeros(1,length(t))];

for i=1:length(t)
    Y(i)=0;
    for j=1:numel(t)
        if(i-j+1>0)
            Y(i)=Y(i)+X(j)*H(i-j+1);
        else
        end
    end
end

figure;

subplot(3,1,1);
plot(t,x);
xlabel('t');
ylabel('x(t)');
xlim([-5 5]);
ylim([-0.5 1.5]);
grid on;

subplot(3,1,2);
plot(t,h);
xlabel('t');
ylabel('h(t)');
xlim([-5 5]);
ylim([-0.5 1.5]);
grid on;

subplot(3,1,3);
plot(t,Y);
xlabel('t');
ylabel('y(t)');
xlim([-5 5]);
ylim([0 1000]);
grid on;