A connection of a noun and a verb is in most cases (not always!) written as two separate words:
Note: This is only true for "Neue Rechtschreibung". Before 1996 you had to write it together: radfahren, schneeschaufeln. Since the combounds are verbs (not nouns), they start with a lower case letter!
But there is an exception: If in the combound expression the "former" noun is not recognized as a noun, then you write both together as one word:
heimkommen (not: Heim kommen) (to come home)
irreführen (not: Irre führen) (to deceive/delude)
preisgeben (not: Preis geben) (to reveal)
teilnehmen (not: Teil nehmen) (to participate)
In the case of "Korrektur lesen" the word "Korrektur" still is recognizeable as a noun, so it is wrong to write it together. "korrekturlesen" ist wrong. "Korrektur lesen" is correct.