the answer is YES.
Before it was discovered, everyone who want to find the area bounded by x=a, x=b, y=f(x) and x-axis, must find it by doing some "limit of sum of f(e) delta(x)."
But since fundamental discovered, we can use integral to find it.
If you want me to write down 3 application of integration in daily life,
all of daily life that need to find area below y=f(x) are the applications.
1- Integration can be traced as far back as ancient Egypt ca. 1800 BC, with the Moscow Mathematical Papyrus demonstrating knowledge of a formula for the volume of a pyramidal frustum.
2- This method was later used in the 5th century by Chinese father-and-son mathematicians Zu Chongzhi and Zu Geng to find the volume of a sphere
3- This method was further developed and employed by Archimedes and used to calculate areas for parabolas and an approximation to the area of a circle. Similar methods were independently developed in China around the 3rd century AD by Liu Hui, who used it to find the area of the circle.