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## Homework Statement

Prove $$T\int_c^d f(x,y)dy = \int_{c}^dTf(x,y)dy$$ where $$T:\mathcal{C}[a,b] \to \mathcal{C}[a,b]$$ is linear and continuous in L^1 norm on the set of continuous functions on [a,b] and

$$f:[a,b]\times [c,d]$$ is continuous.

## Homework Equations

## The Attempt at a Solution

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I couldn't come up with any viable idea. I only know that the integrals are continuous as functions of x.