### Home > APCALC > Chapter 4 > Lesson 4.2.2 > Problem4-57

4-57.

Mateo and Ignacio want to calculate $\int _ { - 2 } ^ { - 5 } f ( x ) d x$ where $f$ is an even function. They know that $\int _ { 2 } ^ { 5 } f ( x ) d x = - 3$. Mateo thinks the answer will be $–3$ while Ignacio thinks the answer will be $3$. Who is correct? Explain.

Graph a possible even function that has the given area.

The boy who was correct paid attention to two things:
1) The fact that $f\left(x\right)$ is even.
2) The order/direction of the bounds.