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Find ##f'(x, y)## where ## f(x,y) = \int ^{x + y} _{a} g = [h \circ (\pi _1 + \pi _2 )] (x, y)## where ##h = \int ^t _a g## and ##g : R \rightarrow R##

Since no differential is given, what exactly are we integrating with respect to?

This looks like a composition of ##h## with some sort of identity operator matrix multiplied by ##(x,y)##, but I'm not exactly sure how it works. I've never this notation used anywhere else.