Let $f(x)$ be the continuous probability density function of a random variable $x$, the probability that $a < x \leq b$, is :
$A.$ This gives the probability at the point of $b-a$ which is not having any significant w.r.t $a$ and $b.$
$B.$ This gives the difference of the probabilities at $b$ and $a$. Note: This is different from cumulative distribution function $F(b) - F(a).$ Ref: https://en.wikipedia.org/wiki/Cumulative_distribution_function
$C.$ This is Probability Density Function. Ref: https://en.wikipedia.org/wiki/Probability_density_function
$D.$ This is expected value of continuous random variable. Ref: https://en.wikipedia.org/wiki/Expected_value
Answer is $C$.
In question f(x) is given probability density function and again the option C is probaility density function .how?
f(x) be the continuous probability density function of random variable X.
Then the probablity be area of the corresponding curve i.e.,