How to solve integrals of non-linear equations, with unknowns in the upper limit of the integral?

Please check the image below for the form of equations. Both the integrals are equal to each other. I have used 'nlinfit' to find the equations F(t), from the available input data. x1 is the unknown, and x2 is 1-x1. To try 'fsolve' I need to have it in the form F(x)=0, which is not in my case. Can someone give a hint on solving this?

Thanks.