the specific heat at constant pressure is the change of Enthalpy with temperature Cp=(dH/dT) so you have to integrate Cp with respect to Temperature. I.e. the change in enthalpy is the area below the the peak inthe DSC measurement. (Be care full to have a stable and flat base line)
There are several free web-Sites dealing with this topic. You may refer to the following ones
This is clearly described in the second reference I sent you (http://pslc.ws/macrog/dsc.htm)
You have to integrate your curve you have obtained with the DSC (the bmp you added to this question). Then you have the area under the curve (take care of the base line!). This area has the dimesion J x K/(g x s). You have to divide this result by the heating rate you used for the measurement (in K/s). Then you obtain J/g. Multiplying this with your sample mass should give you the enthalpy in Joule.
are you sure that you encounter a glass transition? Your attached figurecontains some analysis but the shown tangents look very odd and overall the shown peak should be in my opinion related to melting/crystallization.
Concerning chemical reactions or melting/crystallization the procedure described by Jürgen Hartmann should work.
In general glass transition should not involve delta H in the typical sense. A change in heat capacity is observed which gives you a step in your DSC curve. For some Materials and depending on their thermal history the step is superimposed by a peak which is related to trapped stresses (roughly put). During glass transition the mobility increases and the material can relax.
A comment about your curve: you have two exothermic peaks and not only one. The first small bump is also a heat event. Therefore the integration may not be straightforward because if you integrate the whole peak, you will get the enthalpy sum for two distinct events.
Another strange thing on your curve is that the label says "glass transition". This is definetely not a glass transition but a normal, first order transition (most likely a crystallisation with an associated heat value). A glass transition gives only a step in the curve and not a peak.