Why Does the Integral of 5 from 0 to 1 Equal 5?

[oneamp]

Will someone please remind me why int from 0 to 1 of 5 equals 5, when the sum of the values 5 at, say 1.1, 1.2, 1.3, 1.4, 1.5, 1.6 is > 5? I lost this fundamental understanding today and want to gain it back.

Thank you

 

[olivermsun]

If you go back and think of the integral as an area under the graph, then you see that 5 at 1.1, 1.2, 1.3, ... is always 5, but the boxes are only 0.1 wide, so the area in each of them is only 0.1*5. Add up the 10 boxes and you get the total area which is 5.

 

[oneamp]

Ah yes ok thanks.