Explanation for bond lengths in trans-hexatriene Hexatriene is an unsaturated hydrocarbon with six carbon atoms and five carbon-carbon bonds, three of which are double bonds. 

However, the bond lengths of the $\ce{C=C}$ bonds are not the same. The middle $\ce{C=C}$ bond has a length of 137 pm while the $\ce{C=C}$ bonds at the end of the molecule have lengths of 134 pm, the length of a standard $\ce{C=C}$ bond. The two carbon-carbon single bonds are 146 pm long, also off from the standard 154 pm length of carbon-carbon single bonds.



Clayden's organic chemistry hints that the explanation has to do with the molecular orbits formed and the conjugation system in the molecule. However, I do not fully understand this explanation.

Why do these carbon-carbon bonds show this unusual bond length behavior? A thourough explanation using MO theory would be appreciated.

References

Clayden, J., Greeves, N., Warren, S. Organic chemistry, 2nd ed.; Oxford University Press: New York, 2012.
If you derive the π-type molecular orbitals of hexatriene, the three lower-energy MOs which are filled would look something like this (image from p 33 of Fleming's Molecular Orbitals and Organic Chemical Reactions, Reference Edition):



I suspect what Clayden is getting at is that in the second MO, there is some antibonding character between C3 and C4, whereas the C1/C2 and C5/C6 interaction is purely bonding.