We are going to use the properties of definite integrals. Note that if c belongs to the interval [a,b] and is integrable in [a,c] and [c,b], then f is integrable in [a,b]. Moreover,
[tex]\int_a^cf(x)dx+\int_c^bf(x)dx=\int_a^bf(x)dx[/tex]
Applying this property to the presented case, we obtain that
[tex]\begin{gathered} \int_a^bf(x)dx=\int_{-5}^9f(x)dx+\int_9^{13}f(x)dx-\int_{-5}^2f(x)dx \\ \int_a^bf(x)dx=\int_{-5}^{13}f(x)dx-\int_{-5}^2f(x)dx \\ \int_a^bf(x)dx=\int_2^{13}f(x)dx \end{gathered}[/tex]
Note: Another way to interpret the exercise is to interpret the integral as the area under the curve.
Thus, the answer to the exercise is a= 2 and b = 13.
