Integrand

In $\int_1^4 x^2\,dx$ the integrand is $x^2$, the bounds are 1 and 4, and $dx$ names the variable of integration. Each piece answers a different question about the problem.

Choosing a method is really a matter of reading the integrand's structure: a composition suggests substitution, a product of unlike types suggests integration by parts, and a rational function suggests partial fractions.