Social media and micro-blogging websites have become the popular platforms where anyone can express his/her thoughts about any particular news, event or product etc. The problem of analyzing this massive amount of user-generated data is one of the hot topics today. The term sentiment analysis includes the classification of a particular text as positive, negative or neutral, is known as polarity detection. Support Vector Machine (SVM) is one of the widely used machine learning algorithms for sentiment analysis. In this research, we have proposed a Sentiment Analysis Framework and by using this framework, analyzed the performance of SVM for textual polarity detection. We have used three datasets for experiment, two from twitter and one from IMDB reviews. For performance evaluation of SVM, we have used three different ratios of training data and test data, 70:30, 50:50 and 30:70. Performance is measured in terms of precision, recall and f-measure for each dataset.