How can the capacitor be connected in reverse polarity?
As clabacchio said, some capacitors are unpolarized, so it's perfectly fine to put positive and negative voltages on them.

However, it is still possible to put a AC signal thru a polarized capacitor.  This is done by adding a DC bias of at least half the AC peak-peak voltage.  The entire signal is then still positive, but AC-wise the capacitor acts on it normally.

Nowadays, polarized capacitors are mostly used for bulk storage on power supplies to reduce ripple and to provide short term high current.  A nominal 12V supply, for example, may have 1Vpp AC ripple on it.  That means the voltage is from 11.5V to 12.5V, which is fine for a electrolytic or other polarized cap.  However, the large value of the cap will be applied to providing current to counter the 1Vpp AC voltage swing.

Put another way, polarized caps must always have a positive voltage on them, but there is no such restriction on current.