Convolution for delta function and unit step function

I got an input x(t)= u(t)-u(t-1) and output y(t)= u(t-1)-u(t-2)

I am asked to find the impulse response ,h, by using echo properties,and plot the convolution of x(t) and h(t) with a sampling frequency higher than 500 Hz.

The impulse response,h, I found is delta(t-1), according to the echo properties.

However, I don't get the plot y(t) which supposed to be.

Please let me know how to correct it.

T = 1./500

t=0:T:4;

h[ 0 1 ];

x = (t>0)-(t>1);

y = T*conv(x,h);

plot(y)