BRASILIA/RIO DE JANEIRO, Oct 2 (Reuters) - Brazil's presidential election is headed for a run-off vote, electoral authorities said on Sunday, after President Jair Bolsonaro's surprising strength in the first round spoiled rival Luiz Inacio Lula da Silva's hopes of winning outright.But Sunday's vote, extending a tense and violent election by another four weeks, revitalized his campaign.Although Lula left the presidency 12 years ago with record popularity, he is now disliked by many Brazilians after he was convicted of accepting bribes and jailed during the last election.A career lawmaker turned self-styled outsider, Bolsonaro rode a backlash against Lula's Workers Party to victory in 2018, uniting strands of Brazil's right, from evangelical Christians to farming interests and pro-gun advocates.Lula's proposals for Brazil have been light on details, but he promises to improve the fortunes of Brazil's poor and working classes, as he did as president from 2003-2010, when he lifted millions out of poverty and burnished Brazil's global influence."