dft - Why is the FFT "mirrored"?

If you do an FFT plot of a simple signal, like:

t = 0:0.01:1 ;
N = max(size(t));

x = 1 + sin( 2*pi*t ) ;
y = abs( fft( x ) ) ;
stem( N*t, y )

I understand that the number in the first bin is "how much DC" there is in the signal.

y(1)  %DC

  > 101.0000

The number in the second bin should be "how much 1-cycle over the whole signal" there is:

y(2)  %1 cycle in the N samples
  > 50.6665

But it's not 101! It's about 50.5.

There's another entry at the end of the fft signal, equal in magnitude:

y(101)
  > 50.2971

So 50.5 again.

My question is, why is the FFT mirrored like this? Why isn't it just a 101 in y(2) (which would of course mean, all 101 bins of your signal have a 1 Hz sinusoid in it?)

Would it be accurate to do:

mid = round( N/2 ) ;

% Prepend y(1), then add y(2:middle) with the mirror FLIPPED vector
% from y(middle+1:end)
z = [ y(1), y( 2:mid ) + fliplr( y(mid+1:end) ) ];


stem( z )

I thought now, the mirrored part on the right hand side is added in correctly, giving me the desired "all 101 bins of the FFT contain a 1Hz sinusoid"

>> z(2)

ans =

  100.5943