Uniformly continuous integral example Can someone, please, help me with an example of improper integral of some function
$$\int_{0}^{+\infty} f(x, y)dx,$$ $c \leq y \leq  d$, which is uniformly continuous on $c \leq y \leq  d$, but for which we cannot apply Weierstrass M-test?

Take $f:\mathbb{R}^2 \to \mathbb{R}, f(x,y)=1$. Then f is continuous and in particular uniformly continuous but you cannot dominate it with an integrale function.
