Perform the integral symbolically (by hand or with assistance of symbolic integrator), and enter the result into CVX, presuming it is in compliance with CVX’s rules. If you can’t do this, CVX is not the right tool for your problem.

You will need to get whatever result you get from symbolic calculations into a form which complies with CVX’s syntax and rules. So if your inttegral is a function of x, declare x to be a CVX variable, then write out the function (call the function some time after declaring x a CVX variable) or expression using the character x, so that it will look “normal” to CVX.

It is a non-CVX programming matter how you accomplish that.

The Symbolic Math Toolbox is out of scope of this forum, so you will need to get help elsewhere on how to process solutions from it. But you can first try to manually create the CVX input. If your function does not obey CVX rules, you will be out of luck with CVX. That will certainly be the case if it is not convex.

The point is that you can’t just minimize an arbitrary user-defined function with CVX. You have to be able to write it in CVX form yourself. You are integrating a linear (?) function so it should not be hard. It has to end up convex, too.