Answer
Flexion of the arm at the elbow joint is carried out by the arm flexor muscles in the anterior compartment of the upper arm. These muscles include the brachialis (prime mover) the biceps brachii and the brachioradialis.
For the flexion at the wrist to be possible the arm extensor the triceps brachii in the anterior compartment of the arm must cooperate with the flexors and extend --lengthen. The aconeus also participates (agonist) in extension of the forearm
Work Step by Step
The question asks for muscles involved in flexing and extending the arm. This question is usually asked about flexing and extending the elbow joint , and it is interpreted as such.
The arm includes both upper arm and forearm ; the question is therefore somewhat ambiguous. Upper arm flexors include muscles like the coracobrachialis, the deltoid, and the pectoralis major.The corresponding extensors are the teres major, teres minor, and latissimus dorsi.The author likely meant flexing --reducing the angle-- of the elbow joint.