$$\int\limits_{c}^{d} \int\limits_{a}^{b} \frac{\partial^2f}{\partial x\partial y} dxdy = \int\limits_{c}^{d} \left ( \int\limits_{a}^{b} \frac{\partial }{\partial x} \left ( \frac{\partial f}{\partial y} \right ) dx \right ) dy$$
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Question

$$\int\limits_{c}^{d} \int\limits_{a}^{b} \frac{\partial^2f}{\partial x\partial y} dxdy = \int\limits_{c}^{d} \left ( \int\limits_{a}^{b} \frac{\partial }{\partial x} \left ( \frac{\partial f}{\partial y} \right ) dx \right ) dy$$
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anonymous · Answer

$$\int\limits_{c}^{d}f'(b,y)-f'(a,y)dy$$
=f(b,d)-f(b,c)-f(a,d)+f(a,c)