Measuring Power from Altera Dev. Kit (CycloneIII)
VCCINT is indeed the power to the logic core of the chip. The "banks" refer to the I/O pads, which are divided into groups; each I/O bank can have a different supply voltage for compatibility with different kinds of external interfaces. Those bank VCC connections supply power only to the I/O pads, and have nothing to do with the core logic supply.

To measure the core supply current, you're going to want to remove the jumper and wire the two pins to a low-value shunt resistor. Use your scope in differential (A - B) mode to measure the voltage drop across this resistor, from which you can infer the current. You might be able to solder an SMT resistor directly to the pins of the jumper (on the solder side of the board); then, reinstalling the jumper will simply short it out when not needed for measurements.