In a large skillet over medium heat, heat oil; add carrot and onion.
Cook 5 minutes, stirring occasionally, or until tender.
Stir in pasta sauce and crushed red pepper, heat to boiling.
Reduce heat; simmer, covered, 5 minutes.
Add beans; heat through.
Meanwhile, cook pasta according to package directions; drain.
Spoon sauce over hot pasta; sprinkle with parsley, if desired.