Area from antiderivative of curve to x-axis

[Konglomo]

I'm trying to find the area between the antiderivative of the curve y = 5x3 - 23x2 - x + 3 passing through the point (1, e) and the x-axis from x = 1/√2 to x = 17π/11, to 3 significant figures.
I'm self teaching myself calculus, and this has me stumped.

 

[Redbelly98]

Welcome to Physics Forums.

FYI, I have moved your post to our Homework & Coursework Questions area, since any text-book style question should be posted there, even if it's for independent study and not actual schoolwork.

The way it works on our forums, for problems like this, is: you the "student" show how far you got with the problem, or show what you think is involved in the solution. For this problem, you could work out the antiderivative of y as a starting point...