Neuro-Rule Networks (NRNs) emerge as a promising neuro-symbolic method, enjoyed by the ability to equate fully-connected neural networks with logic rules. To support learning logic rules consisting of boolean variables, converting input features into binary representations is required. Different from discrete features that could be directly transformed by one-hot encodings, continuous features need to be binarized based on some numerical intervals. Existing studies usually select the bound values of intervals based on empirical strategies (e.g., equal-width interval). However, it is not optimal since the bounds are fixed and cannot be optimized to accommodate the ultimate training target. In this paper, we propose AutoInt, an approach that automatically binarizes continuous features and enables the intervals to be optimized with NRNs in an end-to-end fashion. Specifically, AutoInt automatically selects an interval for a given continuous feature in a soft manner to enable a differentiable learning procedure of interval-related parameters. Moreover, it introduces an additional soft K-means clustering loss to make the interval centres approach the original feature value distribution, thus reducing the risk of overfitting intervals. We conduct comprehensive experiments on public datasets and demonstrate the effectiveness of AutoInt in boosting the performance of NRNs.