Hazard function and survival analysis I have a function $\lambda(t)$ which returns the instant probability of dying at a time $t$. I'd like to compute the function $F(t)$ which returns the probability of being dead at a certain time $t$.
Using some reliability theory, I have obtained the following relation:
$$
F(t) = 1-e^{- \int_{0}^{t} \lambda(u) \,du }
$$
But when I do a numerical application I obtain strange results:
Here is the shape of the function $\lambda(t)$:

It can be seen that just after 60 seconds, the probability of dying is above $0.2$. But then when I try to compute the probability of beeing dead at $t=100s$, I obtain:
$$
F(t) = 1-e^{- \int_{0}^{100} \lambda(u) \,du }=0.051
$$
What am I doing wrong?

Answer
Given that your $\lambda(t)$ actually represents the instantaneous probability to die at time $t$ (the hazard), your function $F(t)$ computes the probability to die before a certain time $t$. In other words, $F(t)$ is the cumulative distribution function (CDF) of the time of death.
Following the discussion in the comments, your function represents the probability density function (pdf) $f(t)$ of time of death. From there you can compute the CDF as
$$
F(t) = \int_0^T f(u) du
$$
with $T$ either infinity or the largest possible time.
Some Background on Survival Models / Distributions
The following derivations are largely based on this material
Survival models can be based on the hazard rate $\lambda(t)$ (the instantaneous probability to die at time $t$) or on the distribution of times of death $f(t)$ (which is the pdf of the random variable time of death).
\begin{align}
 \text{Hazard function}   && \lambda(t) &= \underset{\mathrm{d}t \rightarrow 0}{\lim} \frac{P(t \leq T \leq t + \mathrm{d}t | T\geq t)}{\mathrm{d}t} = \frac{f(t)}{S(t)} = - \frac{\mathrm{d}}{\mathrm{d}t}\ln \big[S(t)\big] \nonumber \\
 \text{Cumulative Hazard} && M(t) &= \int_0^t \lambda(x) \mathrm{d}x \label{eq:cum_hazard} \\
 \text{pdf}               && f(t) &= \lambda(t) S(t) \nonumber \\
 \text{cdf}               && F(t) &= P(T < t) = \int_{0}^t f(x)  \mathrm{d}x \nonumber \\
 \text{Survival function} && S(t) &= 1- F(t) = \int_t^{\omega}f(x) \mathrm{d}x = e^{-M(t)} \label{eq:surv}\\
 \text{Life Expectancy}   && e(t) &= \frac{1}{S(t)} \int_t^\omega S(x) \mathrm{d}x \quad \text{with } e(0) = \int_0^\omega S(x) \mathrm{d}x \quad \text{since} \quad S(0) = 1 \label{eq:lexp}
\end{align}
where $\omega$ denotes the highest age.
