A graph of $f$ is shown above. The numbers shown represent the geometric area of each region. Evaluate the following definite integrals.

a) $\displaystyle\int_0^{1} f(x) \, dx$ =

b) $\displaystyle\int_{0}^{2} f(x) \, dx$ =

c) $\displaystyle\int_0^{3} f(x) \, dx$ =

d) $\displaystyle\int_{1}^{2} 8 f(x) \, dx$ =