Write the following expression as a single definite integral of the form \( \int_{a}^{b} f(x) d x \) \[ \int_{-2}^{2} f(x) d x+\int_{2}^{3} f(x) d x-\int_{-2}^{-1} f(x) d x \] SUBMIT ANSWER

The given expression is: \[ \int_{-2}^{2} f(x) \, dx + \int_{2}^{3} f(x) \, dx - \int_{-2}^{-1} f(x) \, dx \] Let's simplify it step by step: 1. **Combine the first two integrals:** \[ \int_{-2}^{2} f(x) \, dx + \int_{2}^{3} f(x) \, dx = \int_{-2}^{3} f(x) \, dx \] This is because the upper limit of the first integral matches the lower limit of the second integral. 2. **Subtract the third integral:** \[ \int_{-2}^{3} f(x) \, dx - \int_{-2}^{-1} f(x) \, dx = \int_{-1}^{3} f(x) \, dx \] This step removes the area from \(-2\) to \(-1\), effectively adjusting the lower limit of the integral. So, the entire expression simplifies to a single definite integral: \[ \int_{-1}^{3} f(x) \, dx \] **Final Answer:** \[ \int_{-1}^{3} f(x) \, dx \]