Interior CT is one of the reconstruction methods from incomplete projection data. In the method, the X-ray passes through only the Region-of-Interest (ROI). The method has various advantages, e.g., the reduction of radiation dose and the application of the large size target. For a long time, the approximate solution has been studied because the interior CT has not the unique solution. Recently, it has been proved that the unique solution for interior CT problem can be obtained if we have a priori knowledge for the ROI. However, the priors in previous studies may have problems for practical application, e.g., difficult to know the true prior or unrealistic assumption to the image. This paper proposes more practical prior assuming piecewise polynomial on an arbitrarily small part of ROI. The uniqueness of the solution in the proposed prior is shown. For practical application, another issue that the placement of the prior region remains. We also propose the method for the placement. The experimental results and the reduction of the artifacts are presented.