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5.12 Rules for combining integrals

Proposition

For integrable functions $f$ and $g$ , real numbers $a,b$ and $c$ , and a constant $A$ , the following hold:

\int(f(x)+g(x))\,dx=\int f(x)\,dx+\int g(x)\,dx;

\int Af(x)\,dx=A\int f(x)\,dx;

\int_{a}^{b}f(x)\,dx=-\int_{b}^{a}f(x)dx;

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