# Basic Properties of Definite Integrals

## Key Questions

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1. ${\int}_{a}^{a} f \left(x\right) \mathrm{dx} = 0$

2. ${\int}_{a}^{b} f \left(x\right) \mathrm{dx} = - {\int}_{b}^{a} f \left(x\right) \mathrm{dx}$

3. ${\int}_{a}^{b} \left[f \left(x\right) + g \left(x\right)\right] \mathrm{dx} = {\int}_{a}^{b} f \left(x\right) \mathrm{dx} + {\int}_{a}^{b} g \left(x\right) \mathrm{dx}$

4. ${\int}_{a}^{b} k f \left(x\right) \mathrm{dx} = k {\int}_{a}^{b} f \left(x\right) \mathrm{dx}$

5. ${\int}_{a}^{b} f \left(x\right) \mathrm{dx} = {\int}_{a}^{c} f \left(x\right) \mathrm{dx} + {\int}_{c}^{b} f \left(x\right) \mathrm{dx}$

I hope that this was helpful.