What is the integrand? And is k_{it} a function of it?

If your integral is \int_{\alpha_1}^{\alpha_2} k_{it}F(\alpha_i)di then you cannot tell as you don’t know the functional form of k_{it}, which depends on i

What is the support of the uniform distribution? Also, it seems you can pull the k_{it} out of the integral, leaving you only with th share of the integral range in the overal support, i.e. (\alpha_2-\alpha_1)/(UB-LB)

I’m sorry I do not know the support. Thank you very much for your reply and help!