Source : Webster's Revised Unabridged Dictionary (1913)

Integral \In"te*gral\, a. [Cf. F. int['e]gral. See {Integer}.]
   1. Lacking nothing of completeness; complete; perfect;
      uninjured; whole; entire.

            A local motion keepeth bodies integral. --Bacon.

   2. Essential to completeness; constituent, as a part;
      pertaining to, or serving to form, an integer; integrant.

            Ceasing to do evil, and doing good, are the two
            great integral parts that complete this duty.
                                                  --South.

   3. (Math.)
      (a) Of, pertaining to, or being, a whole number or
          undivided quantity; not fractional.
      (b) Pertaining to, or proceeding by, integration; as, the
          integral calculus.

   {Integral calculus}. See under {Calculus}.

Calculus \Cal"cu*lus\, n.; pl. {Calculi}. [L, calculus. See
   {Calculate}, and {Calcule}.]
   1. (Med.) Any solid concretion, formed in any part of the
      body, but most frequent in the organs that act as
      reservoirs, and in the passages connected with them; as,
      biliary calculi; urinary calculi, etc.

   2. (Math.) A method of computation; any process of reasoning
      by the use of symbols; any branch of mathematics that may
      involve calculation.

   {Barycentric calculus}, a method of treating geometry by
      defining a point as the center of gravity of certain other
      points to which co["e]fficients or weights are ascribed.
      

   {Calculus of functions}, that branch of mathematics which
      treats of the forms of functions that shall satisfy given
      conditions.

   {Calculus of operations}, that branch of mathematical logic
      that treats of all operations that satisfy given
      conditions.

   {Calculus of probabilities}, the science that treats of the
      computation of the probabilities of events, or the
      application of numbers to chance.

   {Calculus of variations}, a branch of mathematics in which
      the laws of dependence which bind the variable quantities
      together are themselves subject to change.

   {Differential calculus}, a method of investigating
      mathematical questions by using the ratio of certain
      indefinitely small quantities called differentials. The
      problems are primarily of this form: to find how the
      change in some variable quantity alters at each instant
      the value of a quantity dependent upon it.

   {Exponential calculus}, that part of algebra which treats of
      exponents.

   {Imaginary calculus}, a method of investigating the relations
      of real or imaginary quantities by the use of the
      imaginary symbols and quantities of algebra.

   {Integral calculus}, a method which in the reverse of the
      differential, the primary object of which is to learn from
      the known ratio of the indefinitely small changes of two
      or more magnitudes, the relation of the magnitudes
      themselves, or, in other words, from having the
      differential of an algebraic expression to find the
      expression itself.

Source : WordNet®

integral calculus
     n : the part of calculus that deals with integration and its
         application in the solution of differential equations and
         in determining areas or volumes etc.