For document level sentiment analysis (SA), Subjectivity Extraction, ie., extracting the relevant subjective portions of the text that cover the overall sentiment expressed in the document, is an important step. Subjectivity Extraction, however, is a hard problem for systems, as it demands a great deal of world knowledge and reasoning. Humans, on the other hand, are good at extracting relevant subjective summaries from an opinionated document (say, a movie review), while inferring the sentiment expressed in it. This capability is manifested in their eye-movement behavior while reading: words pertaining to the subjective summary of the text attract a lot more attention in the form of gaze-fixations and/or saccadic patterns. We propose a multi-task deep neural framework for document level sentiment analysis that learns to predict the overall sentiment expressed in the given input document, by simultaneously learning to predict human gaze behavior and auxiliary linguistic tasks like part-of-speech and syntactic properties of words in the document. For this, a multi-task learning algorithm based on multi-layer shared LSTM augmented with task specific classifiers is proposed. With this composite multi-task network, we obtain performance competitive with or better than state-of-the-art approaches in SA. Moreover, the availability of gaze predictions as an auxiliary output helps interpret the system better; for instance, gaze predictions reveal that the system indeed performs subjectivity extraction better, which accounts for improvement in document level sentiment analysis performance.