Other Properties of Integrals

Additional useful facts beyond linearity and inverse differentiation.

• Shift by constant: $\int f(x+a)\,dx = \int f(u)\,du$ with $u=x+a$ (captures translation).
• Symmetry hints (for indefinite forms, prepare for definite use).
• Composition caution: no general rule for $\int f(g(x))dx$ without substitution; choose proper methods.
• Integrability: continuity implies integrability; piecewise/with finite discontinuities often integrable (for definite case context).

Summary