Suppose the force of mortality of a person aged $x$ is $\mu_x = \frac{1}{200-x} + \frac{1}{100-x}$ where $x<100$. What is the probability that the person survives at least $t$ more years?
So would this be $\exp \left(-\int_{x}^{x+t} \frac{1}{200-s} \ ds- \int_{x}^{x+t} \frac{1}{100-s} \ ds \right)$
$ = \exp \left(\ln(200-s) |^{x+t}_{x} + \ln(100-s) |^{x+t}_{x} \right)$