The verb 'to correct' is usually transitive, and, as Courtney says, we need to say what we are correcting. "I'll correct it." "Shall we correct our homework?" It can be used intransitively, without an object. However, we do need to add 'for.' Example: (in working out population statistics) "We need to correct for the lack of information from rural areas by extrapolating from last year's data." Or, "Can you please correct for the missing figures." In other words.... make the necessary adjustments. You can use it both transitively and intransitively (with and without an object) in the same sentence. Repetitive, but grammatically correct! "Please can you correct the report by correcting for the missing data." (Please can you amend the report by making the necessary adjustments). I hope this helps a little.

As Courtney says, it doesn't sound complete. At the very least we need an 'it' I'll correct it. Shall we correct it?

No, in both instances the sentences sound incomplete. We must know what you plan to correct. Hope that helps!