problems with integration

[jte]

When writing / reading mathematics, (plain / straight / unbarred) arrows are often used to indicate function domains and codomains (e.g., f:A→B states that f is a function that maps elements of A to elements of B) with barred arrows (↦) used to indicate function rule(s) (e.g., f:ℝ→ℝ, x↦2x) or to state anonymous functions (e.g., x↦2x).