Exploring American history has been a very ________ and exciting business now for three quarters of a century.

The operative word in this sentence is “And”, which implies that the blank must be replaced by a word that gives positive feel. Hence, “Bungling” (unskillful) and “loutish”(clumsy) can be ruled out as both these words convey negative meanings. American history cannot be 'vending' (selling) business as it is being explored neither can it be 'coruscating' (glittering, sparkling) business. Thus, “absorbing “fits our prediction, hence (1) is the answer.