In several practical interpolation problems

the integral values of several subintervals are known

whereas the usual function values at the knots are not given. In this article

we propose an integro quadratic spline interpolation method from the integral values of successive subintervals. First

we use the linear combination of quadratic B-spline functions to satisfy the given integral values and two additional boundary conditions. This problem is equivalent to solving a system of +2 linear equations with a three-band coefficient matrix. Second

we use operator theory to conduct an error analysis and obtain the super convergence order in approximating the function values at the knots. Lastly

we deal with the integro interpolation problem even without any boundary condition based on the linear combination of integral values to approximate the boundary function values. The proposed and modified methods are tested by functions with low frequency in Example 1; the approximation behavior are satisfactory. Meanwhile

the proposed method is tested by functions with high frequency in Example 2; the numerical convergence order is consistent with the theoretical value. The proposed method is easier to implement than other existing methods. The super convergence in approximating function values at the knots is also verified. The proposed method of function reconstruction from the integral values of successive subintervals is universally applicable.