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How do I find the area bounded by the curver y = x^1/2 + 2, the x-axis, and the lines x = 1 and x = 4

I would integrate a dArea as ydx from x=1 to 4

area=INT (x^1/2 + 2) dx from x=1 to 4
area= 2/3 x^3/2 + 2x from 1 to 4

= 2/3 (8-1)+2(4-1) check that, I did it in my head.

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