Thanks, Gianluca, for your insight. Your code works since I had defined the latex string for those special self-introduced integral signs in my notebook before I posted the question here. But the thing is: I do not want to rearrange the boxes by hand and by sight each time I need to do this kind of conversion. Because there can be a ton of integrals of this kind in one notebook of mine. What I need is a way to automate the process, like a function associated with MakeBoxes[] so that every time I do the conversion, Mathematica can recognize it is an integral sign and can not be multiplied into the numerator automatically.
If you have any idea on the automation of the process, I am all ears.