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This paper presents a new symbolic algorithm for polynomial interpolation with integral conditions at arbitrary points. For expressing the integral conditions in the present algorithm, we employ the algebra of integro-differential operators. We also present another algorithm for computing the polynomial interpolation with Stieltjes conditions (combination of general, differential and integral conditions) as a quotient of two determinants. Error due to the formulation of a given function by the proposed interpolation is discussed and its symbolic formulation is presented. This algorithm helps OR would help to implement the manual calculations in commercial packages such as Maple, Mathematica, Matlab, Singular, etc. Certain numerical examples are presented to verify the proposed algorithms.

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