Final answer:
Appointment scheduling requires skill and can be a real art.
Step-by-step explanation:
The first independent clause in the sentence is: "Appointment scheduling, contrary to what you might think, requires skill." This clause can stand on its own as a complete sentence. The second independent clause is: "it should be, and can be, a real art." These two independent clauses are joined together with a semicolon to form a compound sentence.
There are no nonessential clauses or phrases or parenthetical expressions in this sentence.