How to integrate an expression inside simulink block between time t and t+T?

I wish to integrate a mathematical expression inside simulink block which looks something like this-

In order to calculate the definite integral whose bounds vary with every time step in simulink, I integrated the expression inside the integral ,i.e,

using the integrator block of simulink and then added a delay block with time step T. I subtracted the value of signal before and after delay block. I wanted to verify if my approach is right or wrong? Can any expert provide a real way to integrate the above expression. In my problem, the limits of the integration are varying at every time step of simulink environment ,i.e from t-T to t, where t is the time step of simulink environment and T is fixed(lets say T=0.5).

PS: in the integral, capital T is fixed and small t is the time step of the simulink environment. Q and R are fixed matrices of suitable dimension and all other signals namely, x,u are available to me via other simulink blocks.

Thanks for your time and efforts!