# Integration by finding limits?

Integration by finding limits???

Hi Guys, im having a huge problem with integration at the moment and dont know how to approach it cause i have a lousy teacher who couldnt be bothered in actually doing examples on the board. The equation is given as this:

f(t) = 2^t + t^2

Using the equation find the area under the curve between 0 and 1 using:

1) finding certain limits and

2) Fundamental theorem of calculus.

I know how to do 2 as integrating the equation yields 2^t/ln2 + t^3/3 and then sub in the numbers for 1 and 0 and subtract.

Problem is i cant do part 1! Can someone help me with this im desperate. My test is tomorrow!!! Your contribution is much appreciated. Thanks

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$$\int_a^b{f(x)}\, \text{d}x = \lim_{n \to \infty}{\sum_{i=1}^n{f(x_i)} \Delta x$$