The Astronomical Observatory of Brera (INAF-OAB, Italy), with the financing support of the European Space Agency (ESA), has concluded a study regarding a glass shaping technology for the production of grazing incidence segmented x-ray optics. This technique uses a hot slumping phase, in which pressure is actively applied on thin glass foils being shaped, to form a cylindrical approximation of Wolter I x-ray segments, and a subsequent cold slumping phase, in which the final Wolter I profile is then freeze into the glass segments during their integration in elemental X-ray Optical Units. The final goal of this study was the manufacturing of a prototype containing a number of slumped pair plates (meaning parabola and hyperbola couples) having representative dimensions to be tested both in UV light and in x-rays at the Panter facility (Germany). In this paper, the INAF-OAB slumping technique, comprising a shaping step and an integration step is described, together with the results obtained on the manufactured prototype modules: the first prototype was aimed to test the ad-hoc designed and built semi-automatic Integration MAchine (IMA) and debug its control software. The most complete module comprises 40 slumped segments of Schott D263 glass type of dimension 200 mm x 200 mm and thickness of 0.4 mm, slumped on Zerodur K20 mould and stacked together through glued BK7 glass structural ribs to form the first entire x-ray optical module ever built totally composed by glass. A last prototype was aimed at demonstrate the use of Schott glass AF32 type instead of D263. In particular, a new hot slumping experimental set-up is described whose advantage is to permit a better contact between mould and glass during the shaping process. The integration procedure of the slumped segments into the elemental module is also reviewed.