What kind of integration is this and what is the rule behind it?

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I am trying to find out what type of integration is used to solve this problem and what are the rules behind it. I am sorry, if this question is quite basic, but I do not study Mathematics.

The homework problem and its answer

The translation of the text: Test, if this differential form is a full differential. Calculate the finite change dv integrating this differential form from the start of coordinates to the point (a,b) along two tajectories: (0,0)->(a,0)->(a.b) and (0,0)->(0,b)->(a,b).

I would be extremely thankful for any kind of help!

Best regards,

Austėja