Solution
= Solution
Writing $S_i(t)=1-F_i(t)$ for the <survival function>, the definition of the <hazard function> gives
$$
h_i(t)=\frac{f_i(t)}{S_i(t)}
=-\frac{S_i'(t)}{S_i(t)}
=-\frac d{dt}\log S_i(t).
$$
Since $S_i(0)=1$, integration yields
$$
S_i(t)=\exp\left[-\int_0^t h_i(s)\,ds\right].
$$
Therefore
$$
\boxed{\ F_i(t)=1-\exp\left[-\int_0^t h_i(s)\,ds\right]\ }.
$$
The exponent is the negative <cumulative hazard>.