Calabasas-based online banking software provider Digital Insight Corp. has agreed to be acquired by Intuit Inc., makers of TurboTax, for $1.35 billion. The deal, subject to approval by regulators and shareholders, is expected to close in the first quarter of next year. Once complete, Digital Insight Corp. will operate as an Intuit unit with Digital Insight’s Chairman, President and CEO Jeff Stiefler heading up the division. The company’s offices will remain in Calabasas. Mountain View-based Intuit plans to finance the transaction, at $39 per share of Digital Insight stock, with cash and debt. Shares in Digital Insight rose by nearly 16 percent in late trading on Thursday to about $38.20.