Engine oil additives will improve your engine's performance.
This is true -- except that these "additives" have already been added before you buy the oil. Any reputable brand of motor oil will come with additives that improve its viscosity index -- the range of temperatures under which it flows properly through the engine -- and that give it detergent properties that keep your engine free of sludge. Most will also include rust retardants to prevent corrosion and chemicals to protect metallic surfaces.
With all these additives already in the oil, putting in more may actually dilute what's already there and lessen the oil's effectiveness. Check your car's manual to see if it has any special additive needs, but this is unlikely in anything except some of the most exotic high-performance engines.