Finite series tell you how much a (discrete) sequence accumulates. Areas or definite integrals tell you how much a (continuous) function accumulates. More precisely, the integral of f(t) from a to b gives you the accumulation of the "infinitesimal" quantity f(t) dt from t=a to t=b. This will all be clarified we discuss FTC and applications of integrals (such as accumulated change, probability, and slices) later.