Let $f(x)$ be the continuous probability density function of a random variable $x$, the probability that $a < x \leq b$, is :
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$A.$ 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 $C$.
(B) f(b)−f(a) is not CDF.
Reason: Here function f is pdf not cdf.
Note: If X is Discrete RV then P(a≤X≤b) = F(b) - F(a) ,where F is CDF .Both f and F are diffrent.
@Akash Kanase and @Kapil I think selected answer requires small correction.