The development and progress in sensor, communication and computing technologies have led to data rich environments. In such environments, data can easily be acquired not only from the monitored entities but also from the surroundings where the entity is operating. The additional data that are available from the problem domain, which cannot be used independently for learning models, constitute context. Such context, if taken into account while learning, can potentially improve the performance of predictive models. Typically, the data from various sensors are present in the form of time series. Recurrent Neural Networks (RNNs) are preferred for such data as it can inherently handle temporal context. However, the conventional RNN models such as Elman RNN, Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) in their present form do not provide any mechanism to integrate explicit contexts. In this paper, we propose a Context Integrated RNN (CiRNN) that enables integrating explicit contexts represented in the form of contextual features. In CiRNN, the network weights are influenced by contextual features in such a way that the primary input features which are more relevant to a given context are given more importance. To show the efficacy of CiRNN, we selected an application domain, engine health prognostics, which captures data from various sensors and where contextual information is available. We used the NASA Turbofan Engine Degradation Simulation dataset for estimating Remaining Useful Life (RUL) as it provides contextual information. We compared CiRNN with baseline models as well as the state-of-the-art methods. The experimental results show an improvement of 39% and 87% respectively, over state-of-the art models, when performance is measured with RMSE and score from an asymmetric scoring function. The latter measure is specific to the task of RUL estimation.