energy of a transformed signal using Matlab

Below is the code for a compressed and shifted version of x(t) I call y(t). I want to evaluate the energy of the signal y(t) but I am not sure how. I was told I could separate the piecewise into it's parts and integrate them and add the results together. I know the energy of a signal is integral from left boundary to right boundary of the function squared. I am not sure how to set up the boundaries or the integrals here so I would greatly appreciate any help from the gurus.

% 
x = @(t) zeros(size(t)) +(t >= 0 & t < 2).*t.^2 + (t >= 2 & t < 4).*(2*t-8);
y = @(t) (1/2)*x(t+1)+0.5;
t = linspace(0,6);
plot(t,y(t))
axis([-1 8 -4 4])
xlabel('Time(t)')
ylabel('y(t)')
title('Compressed and Shifted x(t)')