Question Details:

Hey guys,

I'm in a pre-analysis course and I have this homework problem over a section that my professor has neglected to cover, so I am really lost. Any help would be appreciated.

Here is the problem

Let f(x,y) be defined and continuous for $\displaystyle a \leq x \leq b$ and $\displaystyle c \leq y \leq d.$, Let

F(x)= $\displaystyle \int_c^d f(x,y) \, dy$

Prove that F is continuous on [a,b].

The book gave the hint "Use the uniform continuity of f." So I went through that since f is continuous and bounded, f is uniformly continuous. From there I'm not really sure where to go.

Any help would be appreciated.

Thanks