Max Integral of Increasing Functions

Let $a \in (0,1)$ and let $\mathcal{C}$ be the set of increasing functions $f:[0,1] \rightarrow [0, \infty)$ such that $\int_{0}^{1} f(x) \, \mathrm{d}x = 1$. Determine: a. $\max_{f \in \mathcal{C}} \int_{0}^{a} f(x) \, \mathrm{d}x$, b. $\max_{f \in \mathcal{C}} \int_{0}^{a} (f(x))^{2} \, \mathrm{d}x$.