The source code of the Java API is freely available. Here's the parseInt() method. It's rather long because it has to handle a lot of exceptional and corner cases.

public static int parseInt(String s, int radix) throws NumberFormatException {
    if (s == null) {
        throw new NumberFormatException("null");
    }

    if (radix < Character.MIN_RADIX) {
        throw new NumberFormatException("radix " + radix +
            " less than Character.MIN_RADIX");
    }

    if (radix > Character.MAX_RADIX) {
        throw new NumberFormatException("radix " + radix +
            " greater than Character.MAX_RADIX");
    }

    int result = 0;
    boolean negative = false;
    int i = 0, max = s.length();
    int limit;
    int multmin;
    int digit;

    if (max > 0) {
        if (s.charAt(0) == '-') {
            negative = true;
            limit = Integer.MIN_VALUE;
            i++;
        } else {
            limit = -Integer.MAX_VALUE;
        }
        multmin = limit / radix;
        if (i < max) {
            digit = Character.digit(s.charAt(i++), radix);
            if (digit < 0) {
                throw NumberFormatException.forInputString(s);
            } else {
                result = -digit;
            }
        }
        while (i < max) {
            // Accumulating negatively avoids surprises near MAX_VALUE
            digit = Character.digit(s.charAt(i++), radix);
            if (digit < 0) {
                throw NumberFormatException.forInputString(s);
            }
            if (result < multmin) {
                throw NumberFormatException.forInputString(s);
            }
            result *= radix;
            if (result < limit + digit) {
                throw NumberFormatException.forInputString(s);
            }
            result -= digit;
        }
    } else {
        throw NumberFormatException.forInputString(s);
    }
    if (negative) {
        if (i > 1) {
            return result;
        } else { /* Only got "-" */
            throw NumberFormatException.forInputString(s);
        }
    } else {
        return -result;
    }
}