I got a 1997 civic HX nd my RPMS were bounicing up and down on idle, so i went nd looked at my IACV (idle air control valve) and one of the hoses are cut (the right one)...does anyone know where that hose goes connected to????

 

if i remember correctly, bottom of the throttle body or to the fast idle valve which is right around that area. just look around for a open nipple in that area.

 

 

how is that hose NOT leaking coolant everywhere

 

This may be old news for you but see this post below.... it may be that the hose goes nowhere after all - I have an Accord 98 where such tube goes nowhere... and it took me hours trying to figure it out until I hit the post below.
The other two hoses are coolant lines and it doesn't matter which of the two you attach which hose: inside is only a chamber where the coolant circulates for those "special cold days".

https://honda-tech.com/forums/search...rchid=25845733