Move between density and CDF

F(t)=∫ from -∞ to t f(x)dx. Outside finite support, the CDF is 0 below it and 1 above it. Where differentiable, f(t)=F′(t). For continuous densities, isolated endpoints have probability zero, so strict and non-strict versions of interval endpoints agree. Check both total area and monotonicity when deriving a CDF.