The value of the definite integral corresponds to the total area of two triangles (see attached plot).
[tex]\displaystyle \int_{-4}^3 \left|\frac x2\right| \, dx = \dfrac12 \times 2 \times 4 + \dfrac12 \times 3 \times \dfrac32 = \boxed{\frac{25}4}[/tex]
