Mathematica integrates over the last iterator first:

Integrate[f[x, y], y, x]

Integrate[f[x, y], {y, Yi, Yf}, {x, Xi, Xf}]

Integrate[f[x, y], {y, Yi, Yf}, {x, Xi[y], Xf[y]}]

For example,consider the difference in

Integrate[Exp[3x], {y, 0, 1}, {x, 0, y}]

(Integrate[Exp[3x], {x, 0, y}])

Integrate[(Integrate[Exp[3x], {x, 0, y}]), {y, 0, 1}]

Compared to

ntegrate[Exp[3x], {x, 0, y}, {y, 0, 1}]

(Integrate[Exp[3x], {y, 0, 1}])

Integrate[ (Integrate[Exp[3x], {y, 0, 1}]) , {x, 0, y}]


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