Calculating total current consumed over time?
For system power consumption it's more normal to write things as either peak or average power consumption in either Watts or amps.
Total power/current is then calculated by multiplying the average power/current by the operating time.

If however you are sure what you want is total current over time then that would be measured in Ah (Amp-hours). It's normally only used when talking about battery capacities rather than system power consumption but I suppose could be useful if you are measuring how much battery you have used. 
The calculation is fairly trivial. Assuming you have a measurement once per second and want the answer in Ah then it's:
Total current at time t = Total current at time t-1 + Current at time t/3600