Write the probability function in terms of its variable. Let this variable be "x."
Write a definite integral of the probability density function with respect to "x." Set the upper limit to "a." Set the lower limit to negative infinity.
Perform the integration according to the laws of integration. You will yield two terms. The second term (the negative term) will equate to zero.
Rewrite the result in the form of a function. Simplify and replace "a" with "x." This is the cumulative distribution function corresponding to the probability density function.
Write the probability function in terms of its variable. Let this variable be "x."
Write a definite integral of the probability density function with respect to "x." Set the upper limit to positive infinity. Set the lower limit to negative infinity.
Perform the integration according to the laws of integration. You will yield two terms, one being subtracted from the other.
Check if the terms equal "1" after performing the subtraction. If so, the probability density function conforms to the rules of a probability density function. Otherwise, it violates the laws of a probability density function and should be revised.
Write the probability function in terms of its variable. Let this variable be "x."
Write a definite integral of the probability density function with respect to "x." Set the upper limit to "a." Set the lower limit to "b." The values of "a" and "b" equal the values of the two numbers to which you want to limit the variable "x." The number "a" must be larger than "b."
Perform the integration according to the laws of integration. You will yield two terms. Both terms evaluate to be real numbers.
Perform the arithmetic as called for in the result of the integral. The final result will be a real number and represents probability P(b < x < a).