Although research on emotion classification has significantly progressed in high-resource languages, it is still infancy for resource-constrained languages like Bengali. However, unavailability of necessary language processing tools and deficiency of benchmark corpora makes the emotion classification task in Bengali more challenging and complicated. This work proposes a transformer-based technique to classify the Bengali text into one of the six basic emotions: anger, fear, disgust, sadness, joy, and surprise. A Bengali emotion corpus consists of 6243 texts is developed for the classification task. Experimentation carried out using various machine learning (LR, RF, MNB, SVM), deep neural networks (CNN, BiLSTM, CNN+BiLSTM) and transformer (Bangla-BERT, m-BERT, XLM-R) based approaches. Experimental outcomes indicate that XLM-R outdoes all other techniques by achieving the highest weighted f_1-score of 69.73% on the test data.