Though it is correct to use a comma before a coordinating conjunction joining independent clauses, this rule should not be extended to other compound word groups.
And links two verbs in a compound predicate: discovered and applied.
And links two subordinate clauses, each beginning with that.
EXCEPTION:If three elements form a compound, commas should be used to separate all the elements.
The phrases beginning with to form a compound direct object and should be separated with commas.
Exercises:
Misuses of the comma 1
Misuses of the comma 2
Related topics:
Commas between independent clauses
Commas in a series