despite what everyone here is saying, it is concievable that the frame rail and fender well needed to be modified.
I've converted a GSR to automatic and because the auto tranny is about 1 1/2" taller than the 5 speed tranny and about 1" longer some body fabrication was necessary.
When I did the conversion, I had to sledge the bottom of the frame rail in about 2" to fit and had to reposition the mount bracket (the bracket that's welded to the frame rail) about 1 1/2" back towards the firewall. Additionally, I had to modify the upper portion of the frame rail to allow the bracket to sit back about 1/2"
What you should do is bolt up ALL the other mounts and check your clearances.
If your tranny is clearing fine, then you should see how the INTEGRA tranny mount is lining up with the Civic bracket. I'm thinking that you may have to change the bracket. I haven't had a chance to compare a 5spd vs. auto civic brackets.
Call your local honda dealer and see if there are different part numbers for the tranny mount bracket between autos and 5spds. If a difference does exist, you may be able to modify the mount. If the brackets are the same you're going to have to change the bracket to an integra one. It isn't that hard.. just a bitch to form the frame rail right. (It took me about 5 hours with a sledge to get the form accurate).