Other problem is that the standard Honda engine in that car had ~170hp. The Ford engine you want to use has ~140hp. So it's going to be a heck of a lot of work to build a slow "Frankenmobile" that's going to be wasted by a stock standard Integra.
As Dave said, anything can be done, the question is, should it be done. In this case, there is zero advantage to using the ford engine in an integra. I could see doing something crazy like putting an Acura 3.2l vtec, or a blown chevy 350, but to go to all that expense, to put a weak 4cyl in that car doesnt make sense.
The things that will need to be done include customized computers (engine vs car), custom wire harnesses so everything works, like tach, oil sensors, air conditioner, etc. custom motor mounts, custom axles/cv joints, custom suspension (possibly), you have to make sure the fuel pressures on the 2 are compatible, custom exhaust, custom air box. Also, you may have issues with registration if you live in an area that requires smog checks
In short, no, its
As the others said is correct, with enough money you can build anything. You can't just buy anything, you would need to custom work everything or since you seem clueless then pay someone to create such a Frankenstein car. I doubt you have a clue you might have to spend $20,000 or more, a really foolish idea dude.
Anything is possible with enough time and money but I'd be willing to bet a lot of money that you'd you'd run out of either before this project was completed. I would try and find something else that is exactly what you want and drives when you pay for it.
I just picked up a 96 integra GSR shell and stupid idea but would be fast.. I'm thinking of dropping in my ford ZETEC engine from a 2000 escort zx2, I was wondering if this is even possible and if so what all I would need to buy to make this fit? It's weird and possibly stupid but it's original and that's exactly what I want. Thanks for any answers!