Answer
True.
Work Step by Step
Given that all the bounds are constant, we can rewrite the iterated integral: $\int_{1}^{2} \int_{3}^{4} x^2 e^y \, dy \, dx = \int_{1}^{2} x^2 \left( \int_{3}^{4} e^y \, dy \right) \, dx = \int_{3}^{4} e^y \, dy \int_{1}^{2} x^2 \, dx$. You can think about it as pulling out the constant $ \left( \int_{3}^{4} e^y \, dy \right) $ from the integral $ \int_{1}^{2} x^2 \left( \int_{3}^{4} e^y \, dy \right) \, dx$.
