Thanks for detailed reply, Nick. I have noticed that my fuel economy has gone down.
When I replaced my air filter and taped the ducting, my engine check light went away. That light came on seven years ago, and my mechanic said it was for the EGR valve, which he said opened and closed too early. He said I needed a new valve, but he said the car doesn't need the part, and so we left it as it is. I always managed to somehow get the light turned off for inspections. One time I took my car in to get the problem fixed to another mechanic, and he said I didn't need a new valve, but just needed to clean it. He charged a bundle, but the light came back two weeks later. That was years ago, and when I went for an oil change recently, the mechanic said my light is on because of the air intake hose. I didn't think much of it because he didn't know the whole story, so I was surprised when the light went off today.
Anyway, I can find the air intake hose on RockAuto, what is hose coming from the valve cover called? I can't find another hose in the "Fuel/Air" section or any other appropriate hose. Is there a name for it?