Equity benchmark indices Sensex and Nifty bounced back from intra-day lows to settle higher on Wednesday, supported by a fag-end buying in market heavyweights Reliance Industries, ICICI Bank and HDFC Bank. After a muted opening, the BSE benchmark swung between gains and losses before settling 271.50 points or 0.38 per cent higher at 71,657.71. The index hit a low of 71,110.98 and a high of 71,733.84 during the session. The Nifty advanced 73.85 points or 0.34 per cent to 21,618.70.