If you never went to prison and have behaved yourself ever since, there's a very good chance you can get this conviction expunged. Then you would not have to list it on any employment application.
Another approach would be to tell a prospective employer the truth: "I committed a felony six years ago, I was sentenced to probation, I was a successful probationer, I did so well they let me off probation two years early, and I really learned my lesson. I could have gone to the joint, and I think about it every day. Six years ago I was a knucklehead, but the judge gave me a break, and I proved him right. If YOU give me a break, I promise you won't be sorry."
Just a thought....
An "expungement" under Penal Code 1203.4 doesn't really expunge anything. You are allowed to withdraw your plea and the judge dismisses the case, but the case will still show up on court records as a case that was dismissed after successful completion of probation.
Although an employer cannot, under California law, inquire about convictions dismissed under 1203.4, it still might show up on a background check. I usually tell clients to disclose the conviction if they think there will be a background check, but note that relief was granted.
Was your felony conviction for a "wobbler" that can be reduced to a misdemeanor? I would ask the judge to do that at the same time.
Note that a conviction for a serious or violent felony under the Three Strikes Law remains a "strike" even if it is reduced or dismissed. If you are convicted of a felony in the future, the judge will not be able to give you probation and your prison sentence would be doubled.