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I was working on a calculus question related to the math subject GRE and I was wondering if it's possible to evaulate this indefinite integral:

[itex]\int {\frac{\sin t}{t}} \, dt [/itex]

The actual question involves Leibniz's rule of differentiating integrals and didn't think of it at the time I worked on it. The main gist of it was finding the local maximum on the interval [itex] (0,\frac{3\pi}{2}) [/itex] of the following function:

[itex] f(x) = \int_{x}^{2x} \frac{sin t}{t} \ dt [/itex]