We present for the first time a study of the 3-200 keV broad band spectra of the bursting atoll source 4U 1728-34 (GX 354-0) along its hardness intensity diagram. The analysis was done using the INTEGRAL public and Galactic Center deep exposure data ranging from February 2003 to October 2004. The spectra are well described by a thermal Comptonization model with an electron temperature from 35 keV to 3 keV and Thomson optical depth, tau_T, from 0.5 to 5 in a slab geometry. The source undergoes a transition from an intermediate/hard to a soft state where the source luminosity increases from 2 to 12% of Eddington. We have also detected 36 type I X-ray bursts two of which show photospheric radius expansion. The energetic bursts with photospheric radius expansion occurred at an inferred low mass accretion rate per unit area of \dot m ~ 1.7x10E3 g/cm2/s, while the others at a higher one between 2.4x10E3 - 9.4x10E3 g/cm2/s. For 4U1728-34 the bursts' total fluence, and the bursts' peak flux are anti-correlated with the mass accretion rate. The type I X-ray bursts involve pure helium burning either during the hard state, or during the soft state of the source.