Because the discrete Fourier transform matches the input signal with complex exponentials and a cosine is the sum of two complex exponentials divided by 2. The same is true of a sine (except it's divided by 2i)
That is where the factor of 1/2 is coming from. Since you have a real-valued signal, if you are only interested in looking at the magnitude, you can just keep the "positive" frequencies and scale them by 2.
T = 0:0.01:10-0.01;
T = T';
x1 = 0.5*sin(2*pi*2*T);
x2 = 1.2*sin(2*pi*5.4*T);
x3 = 0.7*sin(2*pi*7*T);
y = x1+x2+x3;
N = length(y);
duree = max(T)-min(T);
Delta_T = duree/N;
Fe = N/duree;
Delta_F = 1/duree;
xfft = 1/N*fft(y);
magfft = abs(xfft);
magfft = magfft(1:length(xfft)/2+1);
magfft(2:end-1) = 2*magfft(2:end-1);
freq = 0:100/length(y):100/2;
plot(freq,abs(magfft))
grid on;
