Fitting data during its integration

Dear Matlab users,

I try to solve following problem. I have my experimental XY datas and I need to fit this data set by following function:

where P1, E1, A1, P2, E2, A2 are fitting parameters and " beta " and R are the constant and T is the integration variable. I don't know if it is possible to use curvefiting and during this fitting procedure do also integration of this data set.

I will apprieciate any sharing of the simillar experience.

Thank you in advance.