I'm working with a continous dataset that is incomplete and my task is to find the most likely values assuing normal distribution of all data.
I'm given a series of integrals such that $\int^5_{0}f(x)dx = 3$, $\int^7_{25}f(x)dx=20$, $\int^{20}_{30}f(x)dx=8$
Now I'm looking for either mathematical or programmating ways to estimate what is the most likely value of each single integer integral in the dataset, so that: $y_n=\int_{n}^{n+1} f(x) dx$
I'd appreciate any good starting points or recommendations.